President Obama leads in 12 battleground states that will be critical in determining the outcome of the 2012 election, but Mitt Romney has made inroads among independents, according to the latest poll from Purple Strategies.

Obama leads Romney 48 percent to 44 in the 12 battleground states of Colorado, Florida, Iowa, Minnesota, Nevada, New Hampshire, New Mexico, North Carolina, Ohio, Pennsylvania, Virginia and Wisconsin.

The Purple Poll, which focuses on likely voters in swing states, surveyed 1,700 likely voters between April 19 and April 23, and has a 4 percent margin of error.

Many of the data points from previous polling remains the same — Obama has a double-digit lead among women, while Romney holds a slight lead over the president with men. The president’s approval rating also remains steady near the break-even mark, with 47 percent saying they approve against 48 that disapprove.

But there are indications that with Rick Santorum gone from the race and the bruising primary season wrapping up, voters in swing states are beginning to warm to Romney.

The former Massachusetts governor’s historically bad favorability rating has risen significantly since the same poll last month. In March, only 27 percent said they had a favorable view of Romney, compared to 57 unfavorable. In April, those numbers improved to 38 favorable and 48 unfavorable — a 20-point swing.

In addition, Romney has grabbed the lead from Obama among independents in the swing states, 46 percent to 44. Obama had an eight-point lead with independents in the same poll last month.

The economy will be the top issue for voters in the fall election, and poll shows the battle over which candidate is better equipped to handle it is up for grabs.

Thirty-six percent said the economy is getting better, versus 35 that said it was getting worse. Swing-state voters overall gave Obama the edge in dealing with the economy by a margin of 42 to 38, but independents gave the advantage to Romney, 38 to 37.