Bridgeport Hardware Manufacturing Co. of Bridgeport, CT, was founded in 1899, and added official Boy Scout hatchets to their line up in 1934. They produced these official items, in one variation or another, until 1969.
BRIA1A, BSA #1424. Bridgeport made hatchets with an integral handle and head. The hatchet was 11" overall length, with a forged and tempered head and handle. The handle was inlaid with hickory scales, and the head was encased in a leather sheath. The shaft of the axe was wider than the last two versions of this model. The handle had the large words "Official Scout Ax" and the BSA logo on the handle shaft. The BRIA1A was made from 1934 until 1948.

BRIA1A: The May, 1954 Boy's Life still showed the BRIA1A in their advertisement,
though the current hatchet of the day was the BRIA1B.

Bridgeport BRIA1A

BRIA1A: Well used old axe. The electrical tape on the handle is custom, not original. (Courtesy Trent Rock)

BRIA1B, BSA #1424.
BRIA1C, BSA #1424.
BRIA1D, BSA #1424.