I disagree with the previous answer. While the law does not per se preclude a person whose spouse is a felon from attaining POST certification or from employment as a peace officer, practice may yield a different result. The fact is, police employment can be highly competitive and most modern departments engage in very sophisticated in-depth background checks of the candidates for positions. A felony record by one's spouse will likely be revealed during the pre-employment screening, and may affect the strength of your candidacy relative to all of the other applicants for positions in the department. Assuming that you successfully compete for a law enforcement position, in many departments one's spouse's criminal record may also affect the kind of assignments that the department will make.
The degree to which this issue may matter depends entirely on the facts and circumstances of the spouse's criminal history: nature of the charges and underlying facts, how far in the past, single conviction or multiple, etc.
The best way to handle this situation its to be totally honest and forthcoming in the pre-employment interview.
My responses to questions on Avvo are never intended as legal advice and must not be relied upon as legal advice. I give legal advice only in the course of an attorney-client relationship. Exchange of information through Avvo's Questions forum does not establish an attorney-client relationship with me. That relationship is established only by individual consultation and execution of a written agreement for legal services.