How long can a inmate be detained after charges are dropped

Only for the time reasonably necessary to process the paperwork.

First we have a issues with words.

An inmate is a person, already convicted of a crime. They are serving a sentence in a prison. Their conviction is not like charges, (if they have new charges that is different)

If a person is arrested and being held in jail (they are not an inmate but a detainee) if charges are dropped, depending on state law, normally about 24 hours to be released because there is nothing to hold them. Please clarify what is happening

This does not apply to National Security arrests and arrest of terrorist, who appear to be held, with no charges for long periods of time.