The poll, conducted by Massachusetts think tank MassINC for the Boston NPR station WBUR, finds that 46 percent of likely voters in the state said they would vote for Warren, while 43 percent said they would vote for Brown. That's within the poll's margin of error.
The poll is the first to be conducted in the state since early December, but confirms that the race is likely to be a tightly fought one.
The new survey finds that both candidates are fairly popular in the state, although fewer have formed an opinion about Warren -- either because they hadn't heard of her or because they were undecided. Fifty percent of respondents have a favorable opinion of Brown and 29 percent have an unfavorable opinion, while 39 percent of respondents view Warren favorably and 29 percent view her unfavorably.
Brown leads 53 percent to 32 percent among those who have not listed their party affiliation or are something other than Democrat or Republican. Those voters have a mostly favorable opinion of Brown, whereas only 20 percent say they have a favorable opinion of Warren and 35 percent have an unfavorable opinion of her.
In the presidential race, the poll shows that voters would choose President Barack Obama over former Massachusetts Gov. Mitt Romney 55 to 34 percent and would pick Obama over former House Speaker Newt Gingrich 66 to 19 percent.
The new poll was conducted Feb. 6-9 among 503 likely Massachusetts voters, and has a margin of error of 4.4 percentage points.