If a police officer don't arrest for a charge can they come back later and charge you with the charge

Generally, a person can be arrested for a crime anytime until the statute of limitations has run.  The time period for the statute of limitations is set by the state legislature for state crimes and Congress for federal offenses. You didn't specify an offense or the circumstances of the initial encounter with police, so I'll just give an example. In drug cases, the police may conduct an undercover purchase from an individual, and instead of arresting him or her at the time of sale, they keep making buys from the person and arrest after the fourth sale.  If the state where this activity occurs has a statute of limitations on drug crimes of three years, authorities can charge and arrest the person anytime in that three year period. Another example might be a homicide or sexual assault, where the police want to conduct additional investigation such as DNA or other forensic testing before filing charges. In short, the answer is yes, if the police do not arrest you when they first come into contact with you after an offense, they can do so at a later time, so long as the statute of limitations has not run. Jeralyn Merritt, Ask a Lawyer Panelist Since 1998