TREASURIES-Bonds rally as U.S. housing data disappoint

(Adds stock weakness, updates prices)

* Housing starts unexpectedly fall

* U.S. factory output grows in April

* Weaker stocks boosts demand for bonds

NEW YORK, May 16 (Reuters) - U.S. Treasury yields fell on Tuesday after data showing U.S. homebuilding unexpectedly fell in April, adding to recent economic weakness that has raised new doubts about how many times the Federal Reserve will raise interest rates this year. Housing starts dropped 2.6 percent to a seasonally adjusted annual rate of 1.17 million units, the Commerce Department said on Tuesday. That was the lowest since November and followed a downwardly revised rate of 1.20 million units in March.

"People had been anticipating continued strength in the housing market even with rising rates, based on the momentum from 2016," said Jim Vogel, an interest rate strategist at FTN Financial in Memphis, Tennessee. "Traders and investors are going to be sensitive to any indication that there might be more rate sensitivity than people thought," Vogel added.

Benchmark 10-year notes gained 3/32 in price to

yield 2.33 percent, down from 2.36 percent before the data's release. The yields got as low as 2.31 percent as falling stock prices also boosted safe-haven buying of bonds. The weak housing data came after the New York Federal Reserve said on Monday that state manufacturing turned negative for the first time since October, and followed weaker-than-expected U.S. consumer inflation data for April on Friday. Bucking the trend was other data on Tuesday showing that U.S. factory output in April rose at its fastest clip in three years on a surge in auto production. No major economic releases are due on Wednesday. Ten-year U.S. bond yields have largely stayed around 2.20 percent to 2.40 percent since March 22 as investors await further clarity on the Fed's likely path, and whether the Trump administration is nearer to passing tax and fiscal reforms. The measures are expected to boost economic growth, making further interest rate increases more likely. Futures traders have reduced expectations that the Fed will raise rates in June, though that is still viewed as likely. Futures traders are pricing in a 74 percent chance of a June hike, down from 83 percent a week ago, according to the CME Group's FedWatch Tool. Traders see only a 48 percent chance that two or more rate increases will be made by the Fed's December meeting, despite Fed officials repeating that they view two additional hikes this year as likely.

(Editing by Chizu Nomiyama and Richard Chang)