BOSTON (AP) _ Michael Dukakis returned to state business today after winding up his first campaign swing as the Democratic presidential nominee by declaring his party the ''party of jobs ... the party of families.''

Staff members and other workers cheered and applauded as he walked into the executive chamber at the Massachusetts Statehouse today. The governor grinned, bowed and then talked briefly with the group before going into his office.

He was greeted by about 150 supporters who chanted ''Let's Go Mike'' at Logan International Airport late Sunday as he arrived home for the first time since claiming the Democratic banner last week in Atlanta.

He concluded a spirited three-day, cross-country series of campaign appearances with running mate Sen. Lloyd Bentsen of Texas on Sunday by attacking Reagan administration economic policies.

''We're going to win because we are the party of jobs,'' he told a rally at the last stop in Erie, Pa. ''We're going to win, my friends, because we're the party of families.''

Bentsen, who touted his new alliance with Dukakis on the five-state swing from Texas to California and back to the East, returned to Washington and planned to resume campaigning on his own in a few days.

Dukakis was dogged by anti-abortion demonstrators throughout the day, beginning with a Sunday church service in St. Louis where about 100 people protested his support of a woman's right to an abortion. Later in Erie, his route away from the airport was lined with nearly as many anti-abortion protesters.

In Erie, Dukakis appeared with Pennsylvania Gov. Robert Casey in a downtown park where 4,000 to 5,000 people gathered on a hot and sunny afternoon. Citing the decline in steel industry jobs in the region, Dukakis declared, ''We can turn things around, and we're going to do it.''

''It's time to exchange voodoo for can-do,'' he said. ''It's time to exchange trickle-down for building up in this country, and we're going to do it.''

In St. Louis, Dukakis went to services and spoke from the pulpit of the Third Baptist Church with Bentsen and former party rival Rep. Richard Gephardt.

As they entered the downtown church, about 100 anti-abortion demonstrators across the street held up signs and chanted, ''Hey Mike, how many babies did you kill today?''

Dukakis did not acknowledge the protesters but later told reporters his position on abortion has been consistent for 25 years.

''It's a difficult, very serious, very important ethical and moral judgment,'' Dukakis said at a news conference inside the church building. ''But in my judgment it is a woman, in the exercise of her conscience and religious beliefs, that has to make that judgment.

''The question is who makes the decision, and do we go back to the days when we branded a woman a criminal for making that decision,'' he added. ''I believe the vast majority of Americans don't want to go back to those days. They think in the last analysis this is an issue of conscience.''

Dukakis went to the church to underscore a fundamental theme of his campaign i recent days, the commitment to family and community that he spoke of in his speech Thursday accepting his party's nomination.

''The most important thing in my life is family,'' Dukakis told the congregation.

''They are our anchors. They are the place in which we get our strength. It was our parents that gave us our sense of values, sense of ethics, our sense of morality,'' he said.

Bentsen, more conservative on many issues than Dukakis, did not face questioning on the abortion issue. However, spokesman Jack DeVore said Bentsen opposes federal funding for abortion except in cases of rape, incest or when a mother's life is endangered by the pregnancy.