Can absolution be withheld from a murderer until he agrees to give himself up to authorities?

Absolutely not. A priest may withhold absolution from a murderer if he has reason to believe that the penitent is insincere. He also may assign the penitent to atone for his sin by helping those he has harmed, anonymously if necessary. For example, if the victim was a husband and father, the priest may direct the penitent to contribute to the support of the widow and children. In order to avoid revealing the murderer’s identity, the support may be given through the mediation of the parish’s charitable funds. The priest also may encourage the penitent to turn himself in to authorities. But he may not condition absolution upon the murderer’s confession to civil authorities. No one—not even the priest—can require an action that would reveal to outsiders the contents of his sacramental confession and thus violate the seal of the confessional.