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By Hilary Russ and Edward Krudy

NEW YORK, May 13 (Reuters) - A downgrade of Chicago's debt rating to junk created confusion in the $3.7 trillion U.S. municipal bond market on Wednesday, with prices sliding in a volatile session and predictions that they still have further to fall.

While Moody's Investors Service downgraded the city's $8.1 billion of general obligation debt to junk at Ba1, other big Wall Street credit rating agencies have a rosier view of the Windy City.

"Moody's is being much more proactive," said Burt Mulford, portfolio manager at Eagle Asset Management in St. Petersburg, Florida. "But there still is some confusion in the marketplace because of the disparity in the ratings."

Chicago is preparing to issue more debt this month to transform GO variable-rate bonds into fixed rate debt. The city will also borrow another $200 million to pay off related swaps.

The credit ratings gap left some would-be buyers and sellers playing "cat and mouse," testing to see what levels they could get, said John Donaldson, Director of Fixed Income at Haverford Trust in Radnor, Pennsylvania.

"The gap here is so big you're never going to get to that consensus trading level, or at least not easily," he said. "If you end up somewhere in the middle, you get a little apprehensive about hitting the bid too soon and too cheap."

While some Chicago bonds were pricing about 50 basis points higher, at least one potential seller decided not to let go of 7-year bonds at that same cheap level, Donaldson noted. Bond prices usually move inversely to yields.

The city's bonds could cheapen even more as it grapples with its pension funding problem and a potential liquidity crisis.

"Without question, it's not hit rock bottom yet," said Eaton Vance's Tom Metzold. "Financially, they're in a horrible mess. Until they come to grips with that I don't care how vibrant your economy is, you have a financial tsunami of underfunded pension and benefit deficits."

On Wednesday, a sizeable block of insured Chicago Board of Education bonds maturing in 2035 traded at 4.999 percent, nearly 92 basis points higher than the previous day, before the downgrade, according to Municipal Market Data, a unit of Thomson Reuters.

"Traders are looking for a floor," said Casey McGreevy, an analyst at Markit. "I anticipate about a week before the market digests the news and volatility decreases." (Reporting by Edward Krudy and Hilary Russ in New York; Additional reporting by Karen Pierog in Chicago; Editing by Chizu Nomiyama, Meredith Mazzilli and David Gregorio)