Senator Al Franken, Democrat of Minnesota, during an oversight committee hearing in May.

WASHINGTON — A second woman says Senator Al Franken, Democrat of Minnesota, 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.

Mr. 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. Mr. 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 Lindsey Menz, 33, of Frisco, Texas, is the first to involve Mr. Franken’s time as a senator. CNN reported Monday morning that Ms. Renz reached out to the network after Ms. Tweeden went public…