No, except in certain special cases embalming is not required by law. Embalming or refrigeration must take place within 24 hours after death.
A funeral home, mortuary, or funeral chapel would require embalming where there is an open casket or public viewing.
Certain faiths do not believe in embalming.
Airlines do not require embalming either. They require a special container for transfer that allows ice packs to accompany remains for refrigeration.