Yes, the general rule in the U.S., including both California and New York, is that individuals are employed “at will” for an indefinite term, meaning either the employee or employer may terminate the relationship at any time. This is true unless there is a written contract specifying the length of time for the employment (or in some states like California, an oral contract with less than one year of duration is permissible). For all individuals who are employed “at will,” the employer may terminate the employee for any reason, as long as the reason is not prohibited by federal or state law, such as terminations based on discrimination for race, color, religion, sex, national origin, age (40 or older), disability, military or veteran status, or another specifically unlawful basis (“protected classes”). States often expand on the federal protected classes. If a state provides for additional protected classes of individuals, you must follow those laws in the state in which you employ the individual(s).
California expands on federally protected classes by also including: ancestry, immigration status, gender identity, gender expression, marital status, medical condition, and sexual orientation.
New York also expands on federally protected classes by protecting: citizenship or immigration status, creed, sexual orientation, gender identity or expression , marital status, status as a victim of domestic violence, and arrest record or conviction record.