* Boeing down for second session, weighs on airlines
* U.S. consumer prices post first rise in four months
* Apple gains after announcing March 25 event
* Dow dips 0.29 pct, S&P up 0.43 pct, Nasdaq rises 0.65 pct
* British lawmakers to vote on Brexit deal at 3:00 p.m. ET (Updates to afternoon)
By Amy Caren Daniel and Medha Singh
March 12 (Reuters) - U.S. stocks rose on Tuesday after tame inflation data supported the Federal Reserve's dovish stance on future rate hikes, but Boeing's fall for a second straight day in a row pressured the Dow.
The Labor Department said its Consumer Price Index (CPI) rose 0.2 percent last month, in line with estimates, and in the 12 months through February the CPI rose 1.5 percent, the smallest gain since September 2016.
"The takeaway from the data was that inflation is in check and that would allow the Fed to remain patient and that is always good for equities," said Chris Zaccarelli, chief investment officer for Independent Advisor Alliance in Charlotte, North Carolina.
Boeing Co slumped 6.4 percent extending Monday's losses, as more countries grounded the company's best selling line of jets following a second fatal crash in five months, while Senators Mitt Romney and Elizabeth Warren also urged the Federal Aviation Administration to temporarily ground the aircraft.
Airline stocks took a hit with the Dow Jones airlines index dropping 1.43 percent. The broader industrial sector was down 0.77 percent and the only major S&P sector in the red.
"The airlines industry as a whole is now exposed to political pressure and potentially some industry pressure that wasn't there a few days ago," Zaccarelli said.
The world's largest planemaker fell as much as 13.4 percent on Monday and weighed on the Dow Jones index although it pared losses towards the end of the session. All three indexes ended higher boosted by an Apple Inc tech rally.
Apple climbed 1.6 percent on Tuesday and boosted markets, after the iPhone maker invited media to a March 25 event where it is expected to launch a television and video service.
At 12:31 p.m. ET the Dow Jones Industrial Average was down 74.29 points, or 0.29 percent, at 25,576.59, the S&P 500 was up 11.88 points, or 0.43 percent, at 2,795.18 and the Nasdaq Composite was up 49.37 points, or 0.65 percent, at 7,607.44.
Investors are also watching out for developments on the Brexit front. British lawmakers, who rejected May's withdrawal agreement in January, are due to vote on the Brexit deal again at around 3:00 p.m. ET (1900 GMT).
Britain's Prime Minister Theresa May battled to win support for her plans for an orderly Brexit, but Attorney General Geoffrey Cox dealt a blow saying the assurances she had been given still meant the UK could be locked in the bloc's orbit after Brexit.
F5 Networks Inc slipped nearly 7.4 percent, the most on the S&P index, after the network software maker said it would buy privately held NGINX.
Advancing issues outnumbered decliners for a 2.18-to-1 ratio on the NYSE and a 1.62-to-1 ratio on the Nasdaq.
The S&P index recorded 43 new 52-week highs and one new low, while the Nasdaq recorded 50 new highs and 18 new lows. (Reporting by Amy Caren Daniel and Medha Singh in Bengaluru; Editing by Shounak Dasgupta)