My wife and I worked in different states, we are filing federal tax as "Married filing joint", should we file as "Single" on individual state taxes or what should we use?

What status should we use on individual state tax returns? Should we file as Single in each state or Should we file as married filing separately? If we use Married filing separately should we both file tax returns in both the states? States that we worked are Maine and New Jersey. My concern is if we use Married Filing Separately will both these states expect a return from both of us?