(CNN) Across three critical battleground states, the race for president remains tight, according to new CNN/ORC polls in Nevada, North Carolina and Ohio.

 

A new CNN poll finds Hillary Clinton narrowly ahead of Donald Trump in North Carolina and Nevada but continuing to trail the Republican Party's presidential nominee in one of the biggest electoral vote prizes on the map, Ohio.

 

Looking to the downballot races, both are close in North Carolina, with just a 1-point margin between Richard Burr and Deborah Ross in the state's senate race, and Roy Cooper at 49% to incumbent Pat McCrory's 48% in the gubernatorial race there. The senate race in Nevada tilts Democratic, 52% for Catherine Cortez Masto to 45% for Joe Heck, while in Ohio, Rob Portman continues to hold a wide lead over Ted Strickland, 56% to 40%.

 

The polls were taken after accusations of sexual assault against Trump rolled out and the release of a video that has the Republican nominee on a hot mic talking about women in a sexually aggressive and lewd way. 

 

Most voters in these state had heard a great deal about the video but in Ohio and North Carolina it appears these allegations aren't hurting Trump. 

 

In North Carolina, Clinton is up 11 points among women, Trump up 7 points among men. And in Ohio, the gender divide finds women almost evenly split, 48% to 45%, while Trump tops Clinton 52% to 39% among men. The big difference: Married women in Ohio break for Trump, 54% to 40%, while in the other two states, married women tilt the other way. Unmarried women in all three states break in Clinton's favor by a wide margin.

 

College educated whites in North Carolina break sharply in Clinton's favor, 59% Clinton to 37% Trump in North Carolina. They tilt more narrowly toward Clinton in Ohio, 48% Clinton to 44% Trump. 

 

White voters without college degrees remain a core of Trump's support, backing him over Clinton by 48 points in North Carolina, 26 points in Ohio and 25 points in Nevada.  In North Carolina, Clinton's support is bolstered by a 93% to 4% advantage among black voters, about on par with Obama's margin there in 2012. 

 

None of these polls shows Clinton reaching Obama's level of support among younger voters. In Ohio and Nevada, there isn't much of an age gap, though Clinton does fare somewhat better among younger voters than among older ones in North Carolina.

 

There is some evidence in the polls that Trump holds support among white evangelicals 77% in North Carolina and 73% in Ohio back Trump. 

 

Likely voters who back Clinton in Nevada and North Carolina are more set in their choices than are Trump backers in the state, with just 7% of Clinton supporters in Nevada and 6% in North Carolina saying there's a chance they could change their mind by election day. 

 

Among Trump backers, the equivalent numbers are 14% in Nevada and 13% in North Carolina. In Ohio, however, both candidate's supporters are equally likely to say they could change their minds before election day, 12% say they're not set in their choices.

 

Among registered voters overall, Trump's backers are more enthusiastic about voting than are Clinton's supporters in both Nevada (57% extremely or very enthusiastic among Trump backers vs. 48% among Clinton supporters) and Ohio (45% for Trump voters, 38% for Clinton voters). In North Carolina, Clinton holds the edge, 53% to 48%.

 

By a wide margin, voters in all three states say the candidates' positions on the issues will be more important to their vote than the candidates' personal qualities, a judgment that appears to work in Trump's favor. He tops Clinton as better able to handle the economy in all three states, though his advantage is within the survey's margin of error in Nevada, and in Ohio, he also holds a significant edge on handling immigration and trade with other countries. In both North Carolina and Nevada, Clinton appears to have the upper hand on those two issues. In all three states, she has the lead on handling foreign policy, and as better able to handle the responsibilities of being commander in chief.

 

Looking to the downballot races, both are close in North Carolina, with just a 1-point margin between Richard Burr and Deborah Ross in the state's senate race, and Roy Cooper at 49% to incumbent Pat McCrory's 48% in the gubernatorial race there. The senate race in Nevada tilts Democratic, 52% for Catherine Cortez Masto to 45% for Joe Heck, while in Ohio, Rob Portman continues to hold a wide lead over Ted Strickland, 56% to 40%.

 

The CNN/ORC Polls were conducted by telephone on landlines and cellphones from October 10 through 15. In Nevada, interviews were conducted with 1,006 adults, including 862 registered voters and 698 likely voters. In North Carolina, the 1,025 adults interviewed included 929 registered voters and 788 likely voters. And in Ohio, interviews with 1,009 adults included 890 registered voters and 774 likely voters. Results for likely voters in each state have a margin of sampling error of plus or minus 3.5 percentage points, it is 3.5 points for registered voters in Nevada and Ohio, and 3 points for registered voters in North Carolina.