A new poll has former Massachusetts governor Mitt Romney tied with President Obama in Michigan.

In the survey from the Lansing-based EPIC-MRA, which partners with news organizations, Romney takes 46 percent to 45 percent for the incumbent — well within the survey’s four point margin of error. In an April EPIC-MRA poll, Obama received 47 to 43 percent for Romney.

Romney was born and raised in Michigan, and that hometown edge might give him a boost in a state that has been reliably Democratic over the past two decades. Attack ads from outside groups supporting Romney could also be doing the president damage.

According to this poll, while Obama’s support of same-sex marriage appears to be as much of a turnoff in this state as Romney’s opposition to the auto bailout.

Asked about Obama’s position on same-sex marriage, 12 percent said they would be more likely to vote for the president and 34 percent said they would be less likely. Asked about Romney’s position on aid to the auto companies, 18 percent said it made them more likely to support him while 39 percent said it made them less likely.

Yet when asked their choice in light of those positions, the overall breakdown shifts to 46 percent for Obama and 45 percent for Romney. (Again, that’s well within the margin of error.)

The Fix labeled Michigan a “lean Obama” state in our electoral map analysis, as does President Obama. The RealClearPolitics polling average gives Obama a 6.2 point lead. No other survey has shown the race in this state so close:

It’s hard to say whether the race is narrowing or this poll is just an outlier until another survey of the state is done. But Republican outside groups have been spending heavily in the state over the past month, and those attack ads may have had an effect on Obama’s numbers.

According to data from a Republican media buyer, anti-Obama groups have spent over $2.2 million on ads in Michigan in the past month. (You can see a map of spending here.)

Restore Our Future, Romney’s super PAC, has spent $464,800 in Michigan since the beginning of May. Americans for Prosperity, a group backed by the billionaire Koch brothers, has spent $464,800. Crossroads GPS, a group advised by Karl Rove, has spent a little over $1 million, and the American Future Fund (a group tied to an Iowa ethanol businessman) has spent $357,038.

Obama and his allies meanwhile, are not on the air at all — although if more polls like this one come out, that might change.