* Weak US retail sales, inflation data pressure dollar
* Fed hikes rates, outlines plan to reduce bond holdings
* New Zealand dollar slips after GDP growth falls short
TOKYO, June 15 (Reuters) - The dollar nursed losses on Thursday as weak U.S. inflation data left investors wondering if the Federal Reserve would follow up its latest rate hike with another later this year.
Deepening political turmoil in Washington also weighed on the greenback, with the Washington Post reporting that U.S. President Donald Trump is being investigated by special counsel Robert Mueller for possible obstruction of justice.
Also on Wednesday, a prominent Republican was among those shot by a gunman said to be angry with Trump.
The dollar index, which tracks the U.S. currency against a basket of six rivals, was flat on the day at 96.932 but above its overnight low of 96.323 plumbed after downbeat economic figures.
The Federal Reserve raised interest rates a quarter percentage point to a target range of 1.00 percent to 1.25 percent as expected overnight and gave its first clear outline on its plan to reduce its $4.2-trillion bond portfolio.
But the moves were overshadowed by inflation and retail sales data earlier in the day that fell short of market expectations. The core rate of inflation increased at just 1.7 percent on year, the fourth straight monthly deceleration and the slowest overall pace in two years.
The Fed said a recent softening in inflation was seen as transitory, but the latest tepid price readings made investors question its view that the U.S. economy is continuing to improve.
Against its Japanese counterpart, the dollar shrugged off earlier losses and was flat at 109.55 yen, above Wednesday's eight-week low of 108.81 yen.
The euro edged down slightly to $1.1214, below a seven-month peak of $1.1296 scaled overnight.
U.S. 10-year yields were last at 2.134 percent, below their U.S. close of 2.138 percent on Thursday, when they fell as low as 2.103 percent, their lowest since Nov. 10.
The Fed also mapped out a very gradual approach to shrink its $4.2-trillion holdings of Treasury- and mortgage-backed assets that would allow it to begin as early as September. The process could start "relatively soon," Fed Chair Janet Yellen said.
"There is a lot to digest, and even some apparently conflicting signals, such as the fact that the Fed revised its own inflation outlook slightly down and yet kept its intention to raise rates again this year," said Mitsuo Imaizumi, Tokyo-based chief foreign-exchange strategist for Daiwa Securities.
The Fed said it expects U.S. inflation to be at 1.7 percent by the end of this year, down from the 1.9 percent previously forecast.
"It remains to be seen if the Fed can really do both this year - raise rates again, and also begin reducing its balance sheet," he added.
A Reuters poll of 21 of the 23 primary dealers that do business directly with the Fed showed 14 of them now believed it would announce the start of its balance sheet normalization at its Sept. 19-20 policy meeting. The rest of them said it would make such a move at its Dec. 12-13 meeting.
They said they expected Fed policymakers to hike interest rates one more time by the end of 2017 and then three times in 2018.
The New Zealand dollar slipped 0.3 percent to $0.7243 after touching a low of $0.7234, moving away from the previous session's four-month high of $0.7319.
New Zealand's economy grew 0.5 percent in the three months to March, lower than the 0.7 percent growth forecast in a Reuters poll of economists and well below the central bank's forecast for 0.9 percent growth.
(Reporting by Tokyo markets team; Editing by Kim Coghill)