A new poll out today in Michigan from EPIC-MRA shows a much closer race in the state than other recent polling has predicted:

President Barack Obama’s popularity in Michigan has slipped in recent months, leaving him in a dead heat with Republican challenger Mitt Romney, according to a new poll of state voters by EPIC-MRA of Lansing.

The poll, released this morning to the Free Press and four TV stations, shows Romney leading Obama 46%-45%, a reversal from the last EPIC poll in April which showed Obama ahead 47%-43%.

Obama’s personal and job approval numbers also have slipped, with 46% of Michiganders saying they have a favorable opinion of the president, and 41% approving of the job he’s doing.

EPIC co-founder John Cavanagh said the softening in support for Obama is likely related to a robust TV advertising campaign by pro-Romney PACs which have been critical of his handling of the economy. Perhaps most troubling for the Democratic president is a decline in support from independent voters, Cavanagh said.

The EPIC results are in sharp contrast to a poll by North Carolina-based Public Policy Polling late last month which showed Obama leading Romney in Michigan 53%-39%, prompting PPP Director Tom Jensen to suggest the president “won’t have to worry too much about holding Michigan for Democrats” in the fall.

Romney, however, also remains unpopular with many voters (43%), compared to 41% who view him favorably.