A native of Cleveland, Ohio, Perme was one of many major leaguers who saw his baseball career interrupted by a military stint during World War II.

He started his professional career in the Northern League, pitching for the Fargo-Moorhead Twins (1938–1940) and Superior Blues (1941).

In 1942, Perme earned a call-up to the Chicago White Sox in late September after going 15–11 with a 3.22 ERA for Superior.

In a two-season career, Perme posted a 0–1 record with a 3.12 ERA in eight appearances, including one start, giving up six runs on 11 hits and 11 walks while striking out six in 17+1⁄3 innings of work.

Following his brief stint in major leagues, Perme resumed his career in the minors pitching for the Williamsport Tigers (1947–48), Toledo Mud Hens (1949) and Cubs de Drummondville (1951).