Many misdemeanor records are not listed on the national criminal checks at all. Small drug charges and disturbing the peace and other charges might be missed. Many of these misdemeanor convictions started as a heavier charge, possibly a felony, and get plea bargained to a misdemeanor. That would be handy information to know, if they were in the national registry. I have seen Serious Felonies, dropped down to misdemeanors. Disorderly conduct often starts a more serious change.
National criminal checks are better than nothing, but to rely on them is to be disappointed. Do a county level criminal check for all addresses the tenant lived at during at least the last seven years as indicated by their credit report and application.
Remember, this is your investment property. You have a lot of money at risk. Why take a chance. do the best background check you can, and then make the decision. Do not fly blind when accepting tenants! If you have a single family home, it is less of an issue. In a multifamily building, it could lead you to have other tenants move out, and make it difficult to fine new tenants.
Do you ever Google your friends and relatives to see if their mugshot comes up?