The presidential race in the vital state of Ohio has tightened, but President Barack Obama still holds a four-point lead, a CNN poll released Tuesday finds. A New Hampshire poll shows a similar picture.

According to the CNN/ORC International poll (PDF), 51 percent of likely voters in Ohio back Obama, with 47 percent supporting Republican nominee Mitt Romney. Obama's advantage is within the poll's margin of error.   

The survey, released Tuesday, was conducted Oct. 5-8, entirely after last Wednesday's first presidential debate, which was widely regarded as a major win for Romney. Since nonpartisan, live operator polls of likely voters in Ohio conducted before the debate gave Obama a seven- to 10-point edge, the new survey suggests that Romney got a bounce, also seen in national polls.

The CNN poll indicates a huge gender gap, with Romney up by 14 points among men and Obama ahead by 22 points among women.

The American Research Group also came out Tuesday with a poll in Ohio, with Romney leading Obama 48 to 47 percent among likely voters. ARG's previous Ohio survey, conducted in mid-September, had the numbers reversed.

Meanwhile, Ohio Secretary of State Jon Husted, a Republican, announced Tuesday that he will appeal a court ruling that restored access to early voting during the three days before the election, Talking Points Memo reported.

An appeals court ruled Friday that Ohio must treat all voters the same as it treats military members or people who live overseas. Husted called the ruling “an unprecedented intrusion by the federal courts into how states run elections” in a press release on Tuesday.

Obama’s campaign and state Democrats had challenged Ohio’s effort to shorten the early voting period for those who weren’t in the military or based overseas. Early voting was available in the three-day period in 2008, and minority voters were more likely to vote during that period.

In New Hampshire, a poll released Tuesday by WMUR had Romney closing the gap with Obama and trailing by 6 points, compared with Romney's 15 point lag last week.

The poll shows Obama leading 47 to 41 percent, with 9 percent saying they are undecided.