It's been a few years since I worked on this, but at the practice where I managed billing, we required all accounts with credit balances to be reviewed on a monthly basis. We did not contact the patients first before refunding the payments, but we would check the calendar to see if the patient had an appointment coming up in the near future (e.g. within the next 3 months). So for patients with regular visits, we would usually keep the credit on the books and we would flag the account to let the registration staff know that there was a credit and that they should apply that credit to any copay that might be due for the visit, and we'd also wait for the next claim to process to see if the credit could be applied to any patient responsibility due. That process would often resolve a lot of patient credit balances, and also has the advantage that it can potentially help cover the costs of those future services and save having to bill the patient again.
For patients who were not scheduled for any future visits scheduled, or whose credit balances did not resolve through the process above, we would send a refund check. You might want to check your state's consumer credit and protection laws to see if there are any specific rules that apply to your practice regarding credit balances. I think most state laws give you a lot more than 60 days to return funds, although just as a matter of customer service and to avoid accumulation of credits on your practice's accounts, it's a good idea to keep current on these. If patients have moved and you are unable to locate them, you are required to turn those funds over to the state as unclaimed or abandoned property (the legal term for this is 'escheatment') and your state government likely has a web site explaining how this should be done.
Hope this might help some with your questions!