A new Rasmussen poll out Tuesday shows Sen. David Vitter (R-La.) holding onto a double-digit lead in his race for reelection against Rep. Charlie Melancon (D). 

Vitter leads 53 percent to 35 percent with 9 percent of respondents undecided. The automated survey polled 500 probable voters and has a margin of error of +/- 4.5 percentage points.

The poll was conducted after news of the arrest of one of Vitter's legislative aides. Brent Furer was arrested for allegedly assaulting his former girlfriend in 2008. The assault charges were eventually dropped, but Furer pleaded guilty to three misdemeanors. After news outlets reported his arrest last week, Furer resigned but questions lingered over Vitter's knowledge of the events.   

Another lingering issue in the race is the oil spill, with Vitter charging Melancon with backing the Obama administration's six-month deepwater drilling moratorium, which Melancon has repeatedly denied. 

A Rassmussen poll released Monday found overwhelming support for offshore drilling among Louisiana voters — 79 percent still favor it.

-This post was updated and corrected at 12:35 p.m.