Tenant leaves due to noise issues: What does he get back?

[Sam LLoyd]

I have a tenant who has complained about noise a number of times, but does not specify a time or particular noise. The tenants upstairs have kids and a dog, and all the downstairs tenants understand this when they move in.  I've asked him to talk to the neighbor when it gets loud, but he told me he shared unpleasant words with them instead, so I'm doubtful they will try very much harder.  The other tenants downstairs have said either they didn't notice the noise, or it's not nuisance level.  So, I'm not ready to give the upstairs tenants notice of a lease violation, but the downstairs tenant has given me 7 day notice that he's leaving.

Here's the question:  He has been there over 2 years.  The lease is month to month.  I'm pretty sure he won't be paying for this coming month dispite the short notice.  Can I hold the security deposit against unpaid rent?  Or, do I need to give it back (less damages) since he is leaving due to an unresolved issue?

Thanks for your advice.  I've been looking at my lease, and it's pretty solid about what to do if the tenant makes noise, but it all comes down to weather the noise upstairs is a 'health and safety' issue.