Undated (AP) _ Democrats are favored to seize control of governor's mansions in Utah and Indiana and are in close contests with GOP incumbents in North Carolina and West Virginia, as 12 states hold elections for their top office this year.

Taxes and the economy dominate the campaign agenda in many of the states.

Nationally, the gubernatorial lineup is 27 Democrats and 23 Republicans, the roster established April 4 when Democrat Rose Mofford automatically became governor of Arizona upon the impeachment conviction of Republican Evan Mecham.

Incumbents will be on the ballot in nine of the 12 states, with three of four Democrats and six of eight Republicans seeking re-election. Republican Robert Orr of Indiana is barred from a third term, and Democrat Ted Schwinden of Montana and Republican John Sununu of New Hampshire are retiring.

Another Democratic governor may leave office at the end of the year - Michael Dukakis of Massachusetts, who is his party's likely nominee for president. Should he win the election, he would be succeeded by Democratic Lt. Gov. Evelyn Murphy, who would serve until his term expires in 1990.

The other states holding gubernatorial elections are Delaware, Missouri, North Dakota, Rhode Island, Washington and Vermont.

The incumbent in most trouble is Republican Gov. Norm Bangerter of Utah, whose bid for a second four-year term is in grave danger despite a 2-to-1 GOP edge in registration. A recent poll had him trailing Democrat Ted Wilson, former mayor of Salt Lake City, by 23 points.

Bangerter's popularity plummeted after he prodded the Legislature last year into passing a $166 million tax increase, the biggest in Utah history.

His problems have been deepened by the weak economy, the failure of five savings institutions and the drought that made a mockery of his decision to spend $60 million to pump floodwaters from the Great Salt Lake.

''I believe it's winnable, but the governor has got to get his case to the people, his record and what he's done. It's a good case, but we may have passed the point in time where we could salvage the election,'' said former GOP state chairman Charles Akerlow.

Another Republican in some jeopardy is Jim Martin of North Carolina, only the second GOP governor in the state this century. He is locked in a close and colorful race with Democratic Lt. Gov. Bob Jordan.

In a poll taken April 23-26 by Mason Dixon Opinion Research Inc. and published by the Greensboro News & Record, Martin was favored by 47 percent of the voters and Jordan by 39 percent with 14 percent undecided. But after the May 3 primary, a Charlotte Observer poll taken May 18-26 showed Jordan supported by 47 percent and Martin supported by 46 percent.

Martin has accused Jordan of having a ''hidden agenda,'' citing a Jordan speech in which he told black newspaper executives that he agreed with them on some issues he would not discuss publicly for fear of alienating ''rednecks.''

At a debate last month, Martin told an audience he wanted their votes ''regardless of your race, creed or the color of your neck.''

Jordan, a businessman and four-term state senator, has labeled Martin ''the sitting governor,'' with no comprehensive program. Democratic leaders, playing on the theme, last year sent Martin a seat cushion for Christmas.

With Orr retiring in Indiana, Democratic Secretary of State Evan Bayh is hoping to capitalize on his famous name to defeat GOP Lt. Gov. John M. Mutz.

Both campaigns said polls give the 32-year-old son of former U.S. Sen. Birch E. Bayh a lead of nearly 10 points, but Bayh predicted a tight race. ''Democrats win in Indiana - if at all - by relatively small margins,'' he said.

Mutz, who at 52 has almost 21 years of government experience, has made Bayh's youth and relative inexperience a central issue.

In West Virginia, Republican Arch Moore faces a stiff challenge from insurance executive Gaston Caperton, a political novice who spent more than $2 million, mostly his own money, to win a bitter seven-way Democratic primary.

The combative 65-year-old Moore is serving an unprecedented third four-year term. He was governor from 1969 to '77. Democrats outnumber Republicans 2-to- 1.

Coal, glass, oil, gas and steel, backbone industries in West Virginia, are in a slump. The Legislature had to borrow $80 million this year to keep the state afloat, and West Virginia has one of the highest unemployment rates in the nation.

At 48, Caperton advances himself as a new face with a ''business-oriented approach to government.''

''I think it's going to be very close,'' said Priscilla Haden, Moore campaign chairman. ''We're in a Democratic state. I think quite frankly the primary showed some definite anti-Arch Moore vote out there.''

Here is a brief look at the other races:

DELAWARE: Republican Gov. Michael N. Castle faces lawyer and environmentalist Jacob Kreshtool, a wry 69-year-old who in getting the Democratic nod admitted he has not been an active party member, has no money and no staff.

MISSOURI: Republican Gov. John Ashcroft holds a commanding lead in fund- raising and in the polls over state Rep. Betty Hearnes, the likely Democratic nominee. Her husband, Warren Hearnes, was governor from 1965 to '73. According to campaign finance reports filed in June, Ashcroft had raised $2.4 million to Mrs. Hearnes' $321,000. Of Missourians contacted in one recent poll, 60 percent favored Ashcroft and 29 percent Mrs. Hearnes.

MONTANA: Democrat Thomas Judge is attempting a comeback in a campaign focusing on how to ignite a boom in the state, which is beset by a slump in the farm and energy sectors. Judge, governor from 1973 to '81, faces Republican Stan Stephens, a 16-year member of the state Senate. The early GOP favorite, Secretary of State Jim Waltermire was killed in a plane crash two months before the primary.

NEW HAMPSHIRE: Democrat Paul McEachern, a lawyer and a fierce opponent of the stalled Seabrook nuclear plant who nearly rode the issue to the Statehouse against Sununu two years ago, is making another bid. Judd Gregg, a four-term congressman whose father, Hugh Gregg, was governor from 1953 to '55, is considered the clear choice for the GOP nomination by many top Republicans.

NORTH DAKOTA: Democratic Gov. George Sinner is heavily favored to win a second term over real estate broker Leon Mallberg despite a depressed economy and his advocacy of new taxes prompted by low oil and commodity prices.

RHODE ISLAND: Two-term Republican Gov. Edward D. DiPrete holds a commanding lead against Democrat Bruce G. Sundlun, who lost to DiPrete by a 2-to-1 margin in 1986. Sundlun, chairman of a company that owns several TV and radio stations, has never held elective office.

VERMONT: Madeleine Kunin, the state's first woman governor, is favored to win a third two-year term against House GOP leader Michael Bernhardt, who accuses her of taxing and spending too much and pursuing an agenda giving the state too much authority. Kunin has been helped by a rosy state economy. Unemployment is at a record low, while the state has just generated two record surpluses, each $60 million, allowing her to earmark $20 million for land conservation and $7.5 million for a dairy subsidy.

WASHINGTON: Democratic Gov. Booth Gardner, a millionaire former businessman, is strongly favored to win a second four-year term. He has drawn no primary opposition and led his GOP challengers, Norm Maleng, a prosecutor, and state Rep. Bob Williams, by at least 47 points in the latest poll.