WASHINGTON — A second woman says Sen. Al Franken, D-Minn., touched her inappropriately, telling CNN that he grabbed her rear end while her husband took a photo of the two of them at the Minnesota State Fair in 2010.

Franken has been caught up in controversy over allegations by Leeann Tweeden, a radio news anchor in California, that he forcibly kissed her while he was working as a comedian in 2006. Franken has issued an apology and has supported calls from both Democrats and Republicans for the Senate Ethics Committee to investigate.

The new accusation, made by Lindsay Menz, 33, of Frisco, Texas, is the first to involve Franken’s time as a senator. CNN reported today that Menz reached out to the network after Tweeden went public last week, saying that she wanted to share an “uncomfortable” interaction that left her feeling “gross.”

She told CNN that she attended the Minnesota State Fair with her husband and father in summer 2010. Her father’s business was sponsoring a local radio booth, she said, and she spent the day meeting various elected officials and political candidates, including Franken, who was elected in 2008.

When Franken walked into the booth, she said, they had a brief exchange and her husband held up her phone to take a picture of the two of them.

The network quoted her as saying that Franken “pulled me in really close, like awkward close, and as my husband took the picture, he put his hand full-fledged on my rear,” adding, “it was wrapped tightly around my butt cheek.”

Franken issued a statement to CNN, saying, “I take thousands of photos at the state fair surrounded by hundreds of people, and I certainly don’t remember taking this picture. I feel badly that Ms. Menz came away from our interaction feeling disrespected.”

The accusations involving Franken come amid a roiling debate over sexual harassment and abuse that has cost powerful men their jobs in media and the entertainment industry. The question for Franken, now that a second woman has come forward, is whether his political career can survive.

Franken has received support from his female aides; 14 women who have worked for him have issued a statement saying he treated them with the “utmost respect” and “valued our work and our opinions.”