Definition
A civil proceeding that may result in a penalty akin to a criminal penalty, e.g. imprisonment. Little v. Streater, 452 U.S. 1, 10 (1981). The U.S. Supreme Court has described punitive damages as a "quasi-criminal punishment." Pacific Mut. Life Ins. Co. v. Haslip, 499 U.S. 1, 19 (1991). A defendant in a quasi-criminal proceeding is entitled to due process protections.
Illustrative caselaw
See, e.g. Pacific Mut. Life Ins. Co. v. Haslip, 499 U.S. 1 (1991) and Little v. Streater, 452 U.S. 1 (1981).