One can be charged with a misdemeanor without being arrested. Charging is done by a prosecutor, not a police officer. For example, one can be stopped in a store by the store employee for shoplifting. The store employee can record the person's name, address, etc. and let the person leave. Two weeks later, that person may receive a letter to appear in court because he or she has been charged with petty theft. No arrest took place because no police were ever involved in even seeing the shoplifter. However, the person is being charged with a misdemeanor.
A person can be charged with a crime without being arrested. A citation or notice to appear in court can be sent to the person without an arrest taking place.
Once in court, however, most prosecutors will ask for the person to be booked. Being booked is not the same thing as being arrested, but it does mean the person is fingerprinted and photographed just like an aresstee.
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Many people are charged with misdemeanors without being arrested and just served with a summons.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice.
You can be released on citation without being arrested. Usually once you appear in court for the Misdemeanor that was charged by the District Attorney, the court will order you to "book & release". Book & release is the process where they take your booking photo and fingerprints then let you go, once that is done it will appear as an "arrest" on your record, but not before.