Democrats claimed control of the split New York Senate on Tuesday, declaring a quorum after a Republican took a short cut through the chamber because an exterior parlor had been blocked by Democrats for a press conference they never held.

The Democrats voted on about 75 bills stalled by a three-week power struggle and declared them passed. It wasn’t clear if they engineered getting GOP Sen. Frank Padavan on the floor, or simply exploited his presence.

While Democratic Gov. David Paterson initially said he wouldn’t sign any of the legislation, Senate Democratic leaders said it’s up to the clerks of the House and Senate to certify the legislation duly passed, and at that point Paterson should be compelled sign it.

The Democrat-controlled Assembly hadn’t decided Tuesday evening whether to certify them, spokeswoman Melissa Mansfield said.

Paterson ordered the Senate back into a special session at 7 p.m. to take up a handful of time-sensitive bills. They included mayoral control of New York City schools, which was set to expire at midnight. However, with both groups in the ornate chamber, they almost immediately adjourned without passing anything.

“They can have this political fight later,” Paterson said. “We don’t care who the president of the Senate is, but we are affected when the laws expire and people suffer.”

Padavan, a Queens Republican, acknowledged he walked through the chamber earlier Tuesday, but insisted that was before the Democrats’ session started and only because the Senate parlor was blocked. “It’s fraud,” he said of the Democrats’ claim to a quorum.

Sen. Diane Savino, a Staten Island Democrat, said it doesn’t matter if Padavan was just walking through. “As soon as you enter the chamber you’re recorded as present for the day. These are the rules of the chamber,” she said, adding she thought Padavan did it intentionally because there are many important issues at stake.

The Republican senator is an author of the legislation to continue mayoral control of New York City schools. Democratic Sen. John Sampson, a Brooklyn Democrat, is backing a measure that would dilute mayoral control.

New York City Mayor Michael Bloomberg said summer school will be open this morning at the appointed time regardless of what the Senate does. “The chaos, the legal challenges, all the uncertainty, we’ll face that as it comes up,” he said Tuesday.

Blair Horner of the New York Public Interest Research Group described Tuesday’s move by the Democrats as “a lawyer’s dream. It would be a crazy way for the gridlock to be unhinged,” he said. But unless someone has a picture of Padavan in the chamber during the session, there’s probably no way to prove it, he said.

“We’ve got to put this trickery behind us,” said Sen. Pedro Espada, the dissident Bronx Democrat whose alliance with Republicans has divided the chamber 31-31. “We have got to respect the institution.”

Republican leader Sen. Dean Skelos of Long Island called the Democrats’ legislative session “illegal.” He invited their apparent leader, Sampson, to a meeting Wednesday morning to publicly negotiate a power-sharing agreement to cover the next year and a half.

The other Democrats continued voting through the afternoon, with Sen. Andrea Stewart-Cousins presiding and declaring a string of voice votes passed 32-0.

The Senate Democrats defeated one bill to authorize New York City to raise its sales tax to 4.5 percent, from the current 4 percent. The bill, which would have passed easily with Republican support, would make the city and state sales tax 8.875 percent. Bloomberg and the City Council have planned on it to balance the city budget.

Late Tuesday, an appeals court refused to block a judge’s order that the divided senators must convene together to comply with Paterson’s call for special sessions. Paterson has said he’ll keep senators in Albany until they do their necessary work.

Sen. Suzie Oppenheimer, a Westchester Democrat, described Tuesday in terms from “Alice’s Adventures in Wonderland.” “Just when you think things can’t get curiouser,” she said.