In 1931 Connecticut formally adopted a design for the official Arms of the state (a coat of arms or armorial bearings). This design is also featured on the state flag (formally described in 1897), and the state seal uses a variation of it as well. The official description of the Arms:

"A shield of rococo design of white field, having in the center three grape vines, supported and bearing fruit. Below the shield shall be a white streamer, cleft at each end, bordered with two fine lines, and upon the streamer shall be in solid letters of medium bold Gothic the motto: "QUI TRANSTULIT SUSTINET" (He Who Transplanted Still Sustains) "

Source:

The Armorial Bearings: CT.gov

Links:

Cultural Symbols - 50 states
National Seal - state flags - state seals