UNDATED (AP) _ Uncle Sam and the state treasurer aren't the only ones eagerly awaiting your tax return. Battered children, Olympic athletes and furry woodland creatures share begging space with politicians on many state forms.

The response has been grudging. Typically only one taxpayer in 20 will give, and those give up a $5 bill or less. Checkoffs multiply but total donations remain constant.

In big states, however, small contributions can add up to $1 million funds.

''We have done some things that we never could have done with our regular budget,'' said Betsy Wrobel-Boerner of Ohio's Division of Natural Areas and Preserves, which has installed walkways and other visitor facilities in 15 nature preserves with its checkoff money.

Of the 40 states which have income taxes, 36 have at least one checkoff.

Wildlife is the most popular cause, adopted by 33 states. Funds have been used to reintroduce the pine marten in Michigan's Lower Peninsula and peregrine falcons in Minnesota and North Carolina, and to protect Wisconsin's last dozen timber wolves and two nesting female piping plovers.

Programs for abused children come second with 14 states, and campaign fund checkoffs are on the tax forms in 13 states.

The first state checkoffs for political campaigns were enacted in 1973 and Colorado adopted the first wildlife program in 1977, said Corine Eckl, senior research analyst for the National Conference of State Legislatures in Denver.

Other causes include the U.S. Olympic Committee in five states, the Statue of Liberty restoration in Louisiana and New Mexico, domestic abuse programs in Colorado, drug enforcement in Idaho, agriculture education in Montana and a mock legislature for senior citizens in California.

Massachusetts and Rhode Island have checkoffs to help pay for organ transplants, Oklahoma has one for medical care for the needy, and West Virginia is adding a checkoff for adult literacy programs next year.

But why not get the money from the Legislature?

''Ha 3/8 Have you seen the headlines?'' said Ros Harrison of the Iowa Conservation Commission, referring to the slump in the farm state's economy.

Iowa's Chickadee Checkoff raises about $200,000 a year, supporting programs to reintroduce otters and protect barn owls.

The state also has a box for political donations, which was checked by 9.2 percent of its taxpayers in 1985, said Bob Rogers of the Iowa Department of Revenue.

''I think we should limit the use of income tax returns to collecting income taxes,'' says Iowa state Sen. Doug Ritsema. ''There's no limit to the number of worthy, charitable causes that would love to have a checkoff on the tax forms to raise money.''

Louisiana and Illinois now have six checkoffs on their forms.

''If the Legislature approves further checkoffs, we'll have to take the list off the front page, and when that happens, I don't feel we'll collect as much,'' said Shirley McNamara, secretary of Louisiana's Department of Revenue and Taxation.

''We've found that there's only X number of dollars to be donated, and what that (more checkoffs) does is to split up the pie,'' said Jim Crum, director of the non-game wildlife resource division of West Virginia's Department of Natural Resources.

West Virginia's wildlife fund collected $167,203 in 1981, its first year, but the total fell to $75,190 in 1984 when a checkoff for a Children's Trust Fund was added. The children's fund collected $88,440.

Colorado's wildlife fund peaked at $705,700 in donations in 1981, when it was the only checkoff on the form; last year three programs shared a total of $746,476, including $397,533 for wildlife.

Most checkoff programs only permit donations to be deducted from refunds, automatically cutting out those who owe taxes. In Pennsylvania, for example, the average tax refund is only $33, so the potential donation is modest.

Taxpayers are more inclined to give the state's money to political campaign funds than to part with their own. When Montana switched its political fund in 1979 to be deducted from refunds, contributions fell from $70,000 a year to about $4,000.

Contribution rates of about 5 percent were reported in several states, and $5 was a typical gift: $4.40 in Alabama, $4.97 in New York, $4.62 in Minnesota. New Mexico did better with an average gift of $8.28; Colorado had a better than average response of 8.6 percent, but the average gift was $5.86.

Michigan had hoped to raise $1 million a year for its Children's Trust Fund to prevent child abuse, but last year 250,000 taxpayers donated $630,000. Until this year, the donation was limited to $2 on an individual return and $4 on a joint return.

This year, with the lid off, contributions are averaging $5.06.

''The bad news is that that figure represents 5.72 percent of the people who've gotten a refund so far,'' said David Mills, the fund's executive director. ''We'd hoped for 10 or 12 percent.''