Giffords last week visited Newtown, Conn., where a gunman killed 20 young children and six adults at an elementary school last month. The Democrat, who met with families of the victims, was critically wounded two years ago in a deadly mass shooting in Tucson, Ariz.
The Hartford Courant posted images Sunday showing Republican state Rep. DebraLee Hovey's Facebook comments. In one dated Friday she says, "Gabby Giffords stay out of my towns!!"
Hovey released a statement Monday saying her comments were insensitive and that she apologizes if she offended anyone.
Hovey had said in another post that the visit was political.