Quasi-Judicial Proceedings
Three requirements that define a "quasi-judicial proceeding" according to the Ohio Supreme Court for purposes of jurisdiction under RC § 2506.01:
(1) a hearing,
(2) notice, and
(3) the opportunity to introduce evidence;
A quasi-judicial body is an individual or organization which has powers resembling those of a court of law or judge and is able to remedy a situation or impose legal penalties on a person or organization.
Such bodies usually have powers of adjudication in such matters as:
breach of discipline
conduct rules
trust in the matters of money or otherwise.
Their powers are usually limited to a particular area of expertise, such as financial markets, employment law, public standards, immigration, or regulation.
OPINION: Looks like a Municipal Court is a quasi-judicial body with powers to adjudicate Traffic Tickets.
R.C. 2506.01 provides for administrative appeals only from quasi-judicial proceedings.
References: Wikipedia Quasi-Criminal Quasi-Judicial