The incidents happened early Tuesday on Summer Street, between 2 a.m. and 3 a.m.
The man is seen on video breaking into Summer Corner Variety through the back door, and minutes later enters Planet Pizza.
He is described as a white or Hispanic male with tattoos on the backs of both hands. He was wearing a gray hoodie, a black vest and light-colored sneakers.
Anyone with information is asked to call Stamford police at 203-977-4407.