This will depend on the state where you wish to be a crematory operator. First, check with regulatory board in your state to see if there are any special certifications or licenses required for you to work in this capacity. A company that operates a crematory would have you go through the usual employment process which would likely include a background check as well.
Some companies might even require that you are CANA certified due to the legal risks involved in cremation. CANA is the Cremation Association of North America and a very well respected organization in the funeral industry. The details of the CANA Crematory Operator Certification program are listed on their website along with other information that you may find helpful.