ALBANY — New York State is in the throes of a constitutional crisis, with the State Senate having fallen into further disorder after Monday’s decision by a Queens Democrat to flip his allegiances back from last week’s GOP-led coup — creating a 31-31 tie that creates gridlock.

The historic dispute, heightened by the state’s not having a lieutenant governor to break ties, creates a muddled future for how legislation will weave through the partisan-divided Senate—a situation that could remain until the fall elections in 2010.

Left in the wake is a nasty fight over who leads the Senate: Sen. Pedro Espada, a dissident Democrat tapped as the head of the GOP-backed coup, or Sen. Malcolm A. Smith, the former majority leader who Monday found himself deposed of his real power by his colleagues though still claiming the title despite the 31-31 tie.

Talks between the two sides to forge a power-sharing arrangement to get the Senate back in business fell apart quickly Monday evening at the Capitol, with Republicans tossing it to the courts to decide who’s in charge.

“We need judicial intervention. We need judicial clarity,” said Espada, a Bronx Democrat who has claimed the title of Senate president after the June 8 coup in which he and Democratic Sen. Hiram Monserrate of Queens sided with 30 Republicans to take back control from the Democrats.

Monday, Monserrate switched back. By walking away from the negotiating table, the Republicans believe that State Supreme Court Justice Thomas McNamara, who has sent signals that the judiciary is loath to involve itself in a dispute involving another branch of government, will side with them when he issues his ruling, expected sometime today. Appeals are then likely.

In the 62-member chamber, 32 votes are needed to even get a quorum for a Senate session, and the fight now is over who holds the title of Senate president and majority leader.

There are spoils with the posts. The president has control over office space for senators, a not-so-minor matter in a town where square footage and views fuel legislative egos. The president also controls hiring decisions involving Senate staff, and Republicans want to be able to fire staffers Democrats hired six months ago when they took over the Senate following 70 years of GOP dominance.

The Senate president also gets to pick members of various state boards, with the dual benefit of guiding state policy and offering patronage rewards. And, most notably, the president is first in the line of succession if Democratic Gov. David A. Paterson can’t fulfill his term because New York has no lieutenant governor, since Paterson assumed the job after Eliot L. Spitzer resigned as governor in March 2008.

The governor dispatched one of his top aides to court Monday to urge a settlement in order to get Albany back in business. Paterson looked to call a meeting of the sides but backed away after lawmakers said they would meet on their own. For Paterson, the stalemate has halted progress on a number of issues, such as property tax relief.

Democrats said they proposed that the Senate president and floor leaders alternate each day between the two sides and that a six-member panel — three Democrats and three Republicans — be named to determine what bills reach the floor.

Sen. John L. Sampson of Brooklyn, who Monday became the new head of the Democratic conference of senators, said the Republicans were seeking “unreasonable terms” to share power. He said the GOP would not talk about how to pass necessary bills and only wanted to discuss a deal in which the Democrats would agree that the leaders appointed in the coup retain their titles.

“It’s our position that we’re in the majority, and, obviously, the majority has its perks, and they want to be in our position,” Sampson said.

But Sen. Dean G. Skelos, a Long Island Republican who became majority leader in the coup, said Democrats lost that vote when they walked out of the Senate chamber June 8. “It’s not a do-over. They should get a grip on their lives and, quite honestly, understand what’s occurred and come to session and work,” Skelos said.

After he and Espada let Republicans take over the chamber in the coup, Monserrate rejoined the Democrats. “We’ve got to take back the Senate,” Monserrate said as he stood next to his fellow Democrats on Monday.

The flip-flop by Monserrate, under intense pressure, persuaded McNamara to give the sides until this morning to try to resolve the fight. He threatened to rule on the legality of the June 8 vote if no deals were made.

A lawyer for the Democrats said a power-sharing deal is needed. “That requires a lot of negotiations, a lot of give-and-take between the parties, and hopefully that’s what’s about to happen,” Richard D. Emery said.

Asked if such a deal is possible, Emery said, “We’ll see. I’m not the expert in whether 31-31 can work. I don’t think anybody is. It’s unprecedented.”

Monserrate insisted he was not promised any gifts — such as a higher stipend for committee work — for returning to the Democratic fold. He said he found it a “tremendously uncomfortable and tenuous situation” to be part of a coup that included 30 Republicans and only two Democrats. He said he came back after several changes, including Sampson’s becoming Democratic leader.

But because of the 31-31 tie, Sampson cannot formally take the title. Even if the Democrats win their court case and take over the positions of Senate president and majority leader, Smith — the deposed leader — still keeps those titles because neither side would have enough votes to change those titles. But if the Democrats win in court, Smith would be leader in name only, with Sampson running the day-to-day operations.

While Republicans were aglow with the power they said they still hold, Democrats kept using the word “unity.” Privately, however, they know that any such harmony will last only as long as Monserrate, their weakest link, remains happy as a Democrat.