I think Alabama congressmen are immune to traffic tickets while in session.
Just did a quick Google and found this. Don't know for sure but it looks like it might cover this.
http://en.wikipedia.org/wiki/Congressional_immunity
Well...sort of.
The intent of the law was to keep political opponents from using influence with a local sheriff or policeman, in order to keep an opposing member of the state house from getting to the state house in order to vote on an issue. They can't be locked up, but charges can still be pursued, once the legislature is out of session, unless it is a violent crime of some sort.
They can and are issued speeding and parking tickets.
Just ask one Lowell Barron, a legend in his own mind, who once received a speeding ticket from a municipal cop on an Interstate while enroute to a legislative session.
It pissed him off to the point that he introduced a bill making it illegal for municpal cops to enforce speed limits on the Interstate.
The dumb ass (yep, he's a dimwitcrat) didn't word it quite right and even though it passed, it allowed the Sheriff of a county to deputize municipal cops, thus allowing them to once again have jurisdiction on the Interstate.
I think the case you have in mind is one of the erstwhile members of the legislature (one Alvin Holmes...yep, he's a dimwitcrat, and regretably, takes lessons on being a racist bigot from Jihad Cindy, I think), that got caught DUI while the house was in session and tried to get out of the charge under the "no arrest while legislature in session" thing.
Didn't work.
Most states have something similiar, though.