* U.S yield curve flattens for second straight session * U.S. 10-year borrowing cost in repo market at -3.32% * U.S 3-year note auction shows decent demand (Adds new comment, auction results, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, March 9 (Reuters) - U.S. Treasury yields dropped on Tuesday, pulling back from a recent 13-month high on the benchmark note, as investors bought back bonds in a sell-off that market participants have deemed overextended. Since late January, the 10-year yield has risen about 60 basis points. The rally in Treasuries came ahead of an auction of U.S. 10-year and 30-year debt on Wednesday and Thursday, with investors seeking to cover massive shorts on both maturities. Tuesday's auction of $58 billion in U.S. 3-year notes was well received, meanwhile, with the high yield of 0.355% coming below the expected rate at the bid deadline. The bid-to-cover ratio, a gauge of demand, was 2.69, stronger than both the 2.39 ratio in February and the 2.40 average ratio. "The relatively solid 3-year sale brought a big sigh of relief to the Treasury market and yields are moving back down to or near their richest levels of the day," Action Economics said in its blog after the auction. "After the dog of a 7-year sale, there were fears developing that demand for Treasuries is eroding. But this sale dispensed with that notion, at least for today." The U.S. yield curve flattened on Tuesday for a second straight session, with the spread between 2-year and 10-year notes at 137.4 basis points, after hitting its steepest level since September 2015 on Friday. "This the first time since the last few hours of February that we've had four consecutive four-hour periods of stronger prices in the Treasury market," said Guy LeBas, chief fixed income strategist, at Janney Montgomery Scott in Philadelphia. "So there's a good amount of oomph behind the move in prices." In afternoon trading, U.S. 10-year yields were down 5 basis points at 1.543% after rising to 1.613% on Monday, just below their recent peak at the highest since February 2020. Following a surge in short positions, the cost of borrowing 10-year U.S. Treasuries in the repurchase agreement market turned negative in recent sessions and remained that way on Tuesday. The average cost to borrow the 10-year was -3.32% on Tuesday, from Monday's -2.91%. Janney's LeBas said the negative repo rate suggests the current on-the-run, or newer 10-year, notes have a lot of shorts against it. "The auction will probably be a time to close the shorts because the cost of shorting on-the-run 10s are pretty high," he added. Speculators piled into short positions across the Treasury curve last week, adding $45 billion in 10-year net short positions, the largest increase on record, Penglu Zhao, quantitative strategist at TD Securities, said in a note, citing the Commodity Futures Trading Commission data released on Friday. The so-called "belly" of the curve continued to underperform on Tuesday. After five-year yields rose more than longer-dated peers on Monday, they recovered less on Tuesday, down 3 basis points at 0.818%., while the 7-year yield was down 4 basis points at 1.23%. Analysts said the rise in the intermediate maturities - 5 to 7 years - suggested that the market is pricing in an earlier than expected interest rate increase. The eurodollar futures market, which tracks short-term interest rate expectations, has priced in a 90% chance of a rate hike in December 2022, fully pricing in that rate rise by March 2023. Prior to this year's surge in yields, economists on Wall Street had forecast the first rate hike sometime in 2024. March 9 Tuesday 3:02PM New York / 2002 GMT Price Current Net Yield % Change (bps) Three-month bills 0.04 0.0406 -0.005 Six-month bills 0.06 0.0609 -0.002 Two-year note 99-236/256 0.1647 0.002 Three-year note 99-104/256 0.3283 -0.011 Five-year note 98-114/256 0.8197 -0.030 Seven-year note 99-76/256 1.2305 -0.049 10-year note 96-40/256 1.5437 -0.050 20-year bond 95-120/256 2.1558 -0.044 30-year bond 91-184/256 2.257 -0.047 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 8.25 -0.25 spread U.S. 3-year dollar swap 10.25 -0.25 spread U.S. 5-year dollar swap 7.50 -0.25 spread U.S. 10-year dollar swap 1.75 -1.25 spread U.S. 30-year dollar swap -29.50 -2.00 spread (Reporting by Gertrude Chavez-Dreyfuss; Additional reporting by by Yoruk Bahceli and Abhinav Ramnarayan in London; Edited by Alex Richardson and Jonathan Oatis)