How can I find out who lived in my apartment before me?

If the landlord doesn't want to reveal the information, and you can't do a reverse phone search by address (harder these days), the only other place I can think of they might be on record is the town census, available from your town hall.

This isn't really a Real Estate Law question. If you have a problem for any reason (mail coming, people knocking, strange smells), tell the landlord.

... the only other place I can think of they might be on record is the town census, available from your town hall. ...

I don't think the town hall would have the U.S. Census data. You'd have to ask the feds.

True.. I lived in a city that had it's own census, years ago. I looked online and they don't now. Just births, deaths, marriages, etc.

You might try asking the neighbors. They might know.