According to this article,
"Are criminal background checks legal? It appears that they are, so long as the criminal background information is limited to a certain time frame and comes from a reliable source, and is for the purpose of finding past bad conduct which would put other residents or neighbors in a state of potential harm. If you are going to use criminal background checks for screening, I recommend utilizing an established tenant screening company and establish guidelines concerning the nature and age of the past bad conduct."
Here is some useful information about choosing tenants.