Shorter Oxford English Dictionary
1. CAT STICK AD 1626. A stick used in tip-cat and trap ball.
2. CAT - A term used in games esp. a piece of wood tapering at each end, used in tip-cat; also the game itself - First reference AD 1598.
(1) A short piece of wood tapering at both ends used in the game described in 2.
(2) A game in which the tip-cat is struck or tipped at one end with a stick so as to spring up, and then knocked to a distance by the same player - AD 1676.