Levein launched a furious tirade against the ref for two blatant blunders in United's defeat by Rangers at Ibrox.
And despite McCurry admitting he got both decisions wrong Levein could still be in trouble. That stems from the fact he said: "Our last important game was the cup final and we got cheated in that as well."
Peat told MailSport: "The general purposes committee will review the case and decide if Craig should be up before them. We don't tell them what to do but in my eyes using a word like that is criminal."
United have submitted a written complaint over McCurry.
SFA chief Gordon Smith said: "You can criticise decisions but Craig criticised the ref's integrity and that's different."