CEE MARKETS-Zloty falls on politics, demand for Czech bills remains strong

* Zloty near 3-month low vs euro, 5-month low vs forint

* Tension with EU over judiciary reform weighs on zloty

* Czech auction does not underpin fear of demand slackening (Adds Czech Treasury bill auction)

BUDAPEST/PRAGUE, July 27 (Reuters) - The zloty eased on Thursday, under pressure from political tension over Poland's reforms of its judiciary, while more dovish than expected comments from the U.S. Federal Reserve underpinned most Central European currencies.

The zloty traded near 3-month lows against the euro and near 5-month lows against its regional peer, the forint .

It has been hit by bills passed by parliament to allow the government to fire and appoint judges, which triggered street protests and criticism from Brussels.

Polish President Andrzej Duda signed only one of the three bills and unexpectedly said he would veto the other two.

But the European Commission said on Wednesday that it would launch legal action against Poland over the reform which undermines the independence of judges.

The zloty traded at 4.2559 against the euro at 1245 GMT, down by about 0.1 percent. The forint, meanwhile, which is a frequent regional trade against the Polish unit, firmed by 0.3 percent to 304.73 versus the euro.

The political tension does not allow the zloty to strengthen despite the region's good economic fundamentals, analysts said.

"Increased political uncertainty stemming from the emergence of the conflict between the president and the government in Poland and fears about the effects of the EC actions against Poland may weigh on the zloty... despite the dovish Fed," Bank Zachodni WBK analysts said in a note.

The Fed's comments cemented expectations that it will start unwinding its massive bond holdings in September, but that might lessen the need of rate hikes, therefore the dollar continued to ease in its crosses.

Central European government bonds and stocks were mixed and mostly rangenbound.

The Czech crown also eased a shade.

Demand stayed strong at an auction of Czech 8-week Treasury bills, showing foreign investors remained interested in Czech debt markets before large redemptions in short-term bills in the coming months, which some analysts said was a risk to the crown.

Investors flooded markets with tens of billions of euros before the Czech central bank abandoned a cap on the crown in April, betting on crown strengthening once it was free.

Some analysts say this could be a factor in the central bank opting for a rate hike as more than 150 billion crowns of T-bills come due in August and September. If foreign investors exit those positions it would weaken the crown, posing an upside risk to inflation.

Other analysts, though, see an increase in the Czech Republic's weighting in JP Morgan indices earlier this year helping keep foreign money in Prague. (Additional reporting by Warsaw editorial; Editing by Keith Weir and Pritha Sarkar)