ALBANY - Senate Majority Leader Dean Skelos started this skirmish with Alec Baldwin. Now -- thanks to Twitter -- it seems it won't stop.

The liberal celebrity and the New York Legislature's top Republican traded barbs for a second day, competing Wednesday via the social networking site. Skelos (R-Rockville Centre) called Baldwin a "hypocrite" for supporting Occupy Wall Street protesters and "raging" against corporate profits, while doing commercials for a major credit card company.

Baldwin called Skelos a "Republican tool" and a "professional" twister of facts, and challenged him to appear at a joint news conference -- with his tax returns in hand.

"C'mon Dean Skelos!! You professional distorted [sic] of facts!!" Baldwin wrote on Twitter at the heat of the exchange. "Join me in a press conference. And bring your tax returns!!"

It all began a day before during a radio interview about the Occupy Wall Street protest. Skelos was drawn into a question about its cousin, Occupy Albany, a much smaller group that has set up tents in a park across from the State Capitol and called for reinstatement of the "millionaires' tax." Skelos repeated his long-held opposition to that idea and then took a shot at Baldwin, who recently stopped by the Occupy Wall Street encampment.

"We can't be influenced by the Alec Baldwins of the world that are just buying a $17 million condo in Greenwich Village, and he's going to tell us that we should tax everybody else," Skelos said. (It was actually $11.7 million.)

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And the gloves came off.

"Only a Nassau County Republican tool like Dean Skelos could drag my name into a debate on state income tax," the "30 Rock" star began, before getting worked up. "I pay more in income txs [taxes] in 1 yr than Skelos pays in 20. So what's his point?"

"If . . . [Baldwin] thinks I'm wrong, he must think Gov Cuomo is too since he agrees with me u can't raise taxes on businesses, working people," Skelos replied.

"I challenge Dean Skelos 2 a Citizen's Responsibilities Contest. Provide ur tax returns and personal itinerary for the past ten years," Baldwin continued. "Then let's see who has done more for their communities."

"Hypocritical. [Baldwin] rages against corporate greed yet is a paid spokesperson for corporate giant Cap [Capital] One," Skelos rejoined.

Baldwin then issued the debate challenge. Skelos responded with an attempt to tone it down and end things with a reference to Baldwin's TV character: "BTW, think Jack Donaghy gets together with Liz Lemon in the end."

Things slowed down after that. In an apparently final, so's-your-old-man type of parting shot, Baldwin concluded: "I know some folks at the Wagner School when you're ready to brush up on tax policy."