UPDATE 1-NY state Senate Democratic-GOP brawl continues

* NY senate Republicans meet but can't enact bills

* Judge rejects Democrat bid to block GOP from leadership

* NY AG Cuomo may probe why Democrats switched sides (Adds comments by governor and Cuomo, paragraphs: 11, 15-16)

ALBANY, June 11 (Reuters) - The New York state Senate's Republicans held a session on Thursday but could not enact any bills, as a leadership dispute with the Democrats showed no signs of letting up.

Democrats lost the first round in a court fight to block the GOP, who claim to have won leadership of the Senate after forcing a vote on Monday and winning over two dissident Democrats.

The political fight has left unresolved hundreds of bills affecting the finances of cities and towns around the state, from New York City's sales tax hike to the City of Yonkers extension of a real estate-linked tax. State bills on subjects ranging from gay marriage to a spending cap to pension reforms are also hanging.

Senate Republicans, who faced a gauntlet of shouts and shoves by protesters when they entered the chamber, say they won the leadership by a vote of 32 to 30 on Monday.

But the Democrats said their opponents violated state law by usurping their majority leader and broke Senate rules.

The tussle prompted blistering editorials and tabloid front covers, such as Tuesday's Daily News: "No End to the Shame."

One rebel Democrat, Senator Hiram Monserrate, was indicted for a felony assault. The other, Senator Pedro Espada, who becomes Senate President if the Republican coup holds, has paid costly campaign violation fines and is being probed over a non-profit group.

Supreme Court Judge George Cerisa of Troy on Thursday rejected the Democrats' motion for an injunction to stop their rivals.

"I don't have the power to issue a restraining order such as is being sought here," the judge said in a ruling broadcast by local cable TV station NY1.

A spokesman for Democratic Senate Majority Leader Malcolm Smith said the Democrats have now appealed to an Albany-based judge. The Democrats won control of the Senate in the November election for the first time in four decades.

Democratic Attorney General Andrew Cuomo might scrutinize what led the two Democrats to switch. Asked about investigation requests from both parties, Cuomo told reporters he had not heard that Republicans had contacted his office, but added: "We have had discussions about possible allegations of wrongdoing and this office will proceed as we deem appropriate."

The Republican coalition showed signs of fraying as one of the two Democrats declined to vote.

Monserrate, noting there was nothing to vote on because the Democrats refused to release the legislation, called bill jackets, left the chamber, saying he wanted to recruit more Democrats to cross party lines.

His fellow rebel, Espada, said that in a telephone call Governor David Paterson acknowledged him as Senate President and Republican Senator Dean Skelos as Majority Leader.

However, a spokeswoman for the Democratic governor said Espada was incorrect. "He spoke with Espada but did not acknowledge him as the new senate leader," she said by email.

"The governor still recognizes the Democrats as the majority party...and urges the Senate to work it out and get back to the people's business," she said. (Reporting by Elizabeth Flood Morrow in Albany and Joan Gralla in New York; Editing by Chizu Nomiyama)