Previous research studies how private protection can be a substitute for public protection (policing) services. This paper looks carefully at situations in which public and private protection are complementary, that is, when private protection must be coordinated with public protection to be effective. For example, home alarms deter theft by being connected to a local police station: if the police do not respond to a home alarm, the home alarm on its own is virtually useless in halting a crime in action. We show that very different optimal policy recommendations are generated when public and private protection are substitutes versus when they are complements.