Constantine permitted transfer of legal cases from civil to ecclesiastical courts, and also permitted ministers to manumit slaves. Both, Potter says (Constantine the Emperor, 181), were steps that effectively turned clergy into civic authorities.
On the first decision, Potter notes that “The main problem with Constantine’s decision, from a Christian perspective, was that Christians traditionally had a very different understanding of the role their bishop ought to play: ideally he was a person who aimed at restoring a damaged community, unlike the judge or arbitrator of the pagan world who was supposed to hold for one side or the other.” Potter wonders whether “Constantine was aware of the difference.”
Regarding manumission, Constantine gave bishops and priests “permission to create Roman citizens out of slaves.” The edict hedged in the permission, indicating that the freed slave became a citizen only if manumitted before the gathered people. Still, a civic authority was granted to the church.
This is “Constantinism” in detail: The church is being knit into the civic order of Rome. It likely worked the other way too, though: Civic responsibilities carried out by the church were leavened with the gospel; bishops presiding over court cases would bring their habits of fairness and their instinct to repair with them.