* Greek T-bill auction well-covered but with high yield
* Analysts say Greece still has tough times ahead
* Traders look ahead to Bernanke's testimony on Wednesday (Recasts, updates prices, adds comment, byline)

NEW YORK, April 13 (Reuters) - The euro fell against most currencies on Tuesday as a Greek debt auction highlighted persistent doubts about Greece's credit risk and investors worried about tepid economic prospects in the euro zone.

Greece passed its first borrowing test since the euro zone agreed on a potential rescue package but paid a high premium to issue the Treasury bills.

That showed investors remain unsure Greece can handle its debt crisis alone. Such concerns could drive Athens to take the aid lifeline agreed by euro zone finance ministers.

Even though we had a pretty good Greek auction today, people are still finding few reasons to buy the euro in the medium term, said Vassili Serebriakov, senior currency strategist, at Wells Fargo in New York.

Growth prospects are still quite subdued in the euro zone compared to that of the U.S. That's what really preventing a strong bounce in the euro.

In early afternoon trading, the euro was trading at $1.3581, slightly down on day and off a session high at $1.3626.

Greece easily sold its allocation of 6-month and 12-month T-Bills, raising 1.56 billion euros, with the inclusion of non-competitive bids, but at a yield which was costly for the debt-laden country. [ID:nLDE63C0FQ]

The euro rose briefly in the immediate aftermath of the auction as traders reacted to a strong bid-to-cover ratio, but weakened subsequently as markets became cautious about the euro zone's medium-term outlook.

Even if we assume that Greece and the Euro zone muddle through this crisis and Greece avoids default, there should be permanent damage to the euro, said David Gilmore, a partner at FX Analytics in Essex, Connecticut

Greece has exposed two key flaws in EMU (European Monetary Union)...monetary union without political union and economic divergence with one monetary policy. I don't forecast a Greece default, just a rising cost for Eurozone for keeping Greece in EMU.

On Monday, the euro climbed to a near one-month high of $1.3691 after euro zone finance ministers agreed on an aid package for Greece, before paring gains as investors sought clarification about the plan.

The euro also slipped 0.1 percent against the yen to 126.52, and fell 0.4 percent against the Swiss franc to 1.4331 EURCHF=.

The dollar, meanwhile, drifted lower against a basket of currencies .DXY as investors grew nervous about Federal Reserve Chairman Ben Bernanke's testimony on the economic outlook before the Joint Economic Committee.

Earlier in the session, there was speculation among traders that Bernanke might use that forum to talk about normalizing the spread between the fed funds and discount rates. that boosted the dollar against the euro specifically, which traded from around $1.3600 down to $1.3550.

Against the yen, the dollar was down 0.1 percent at 93.15.

The draft of a policy paper from Japan's ruling party, released early in the European morning, initially put the Japanese currency under pressure before focus shifted to other risks and events.

The draft suggested the dollar should be kept around 120 yen. This pushed the greenback to the day's high at 93.42 yen. [ID:nTKG006692]. (Additional reporting by Nick Olivari; Editing by Andrew Hay)