Authorities say the 36-year-old clerk at a Cumberland Farms in Shelton saw a man put the signs into an SUV shortly after 1 a.m. Tuesday.
Police say the worker was struck and dragged by the SUV and landed on his head.
Police say the clerk is hospitalized in critical condition, and authorities are looking for the suspects. The employee's name hasn't been released.
Hasselhoff starred in the TV shows "Baywatch" and "Knight Rider."
The signs featuring him advertise iced coffee.
Cumberland Farms officials say more than 500 of them have been stolen from stores in several states in recent months.
