Whether or not required by law, I think it is prudent to do so. It will give your tenant some peace of mind at the beginning of a (hopefully) long business relationship with you. I also think it makes you come off as a professional, rather than a "mom and pop."
Secondly, if there is a larceny (or worse), you want a clear conscience (and no culpability) if you are ever asked by LE or courts whether you changed the locks or not.
I know some people on here don't like them, but I have had good results with the Kwikset Smartkey system, which makes this a 30 second job.
It's really a small price to pay for great return via goodwill and safety.
New locksets are cheap enough. once you swap it out, save the old set and then put it back on in a couple years. You can get 2 or 3 sets and rotate through them so every tenant gets a new key.
Change the locks. It's a basic industry standard to do so. Don't reuse the old lock in the same unit, even if you wait several years, as those who've had keys previously just might try to enter the unit at a future time. Not worth the risk to the current tenant and not worth the risk to you.