I am the lease owner of an apartment. My former roommate moved out 37 days ago and left all of his belongings. I have tried numerous times to contact him and he will not return any of my calls, text messages, or e-mails. What can I legally do with his belongings?

After 30 day written notice I think you can do anything you want with them.
I am not sure that e-mail would be sufficient enough for written notice.
You might want to send a certified letter.

Send him a letter by certified mail, return receipt requested, to his last known address. Tell him that if he doesn't pick up his belongings within the next 30 days you will dispose of them.