When my tenant vacates, do I have to give interest along with the security when they leave?

In many states, the law requires that a landlord pay interest on security deposits held by the landlord for a residential lease.  In Connecticut, the laws pertaining to this obligation are overseen by the Department of Banking.  That Department provides the following information about a landlord's obligation to pay interest on a residential security deposit: 

Do Landlords Pay Tenants Interest On Security Deposits?

Yes. Landlords must pay tenants interest on security deposits of at least the average commercial banks savings deposit rate as annually determined and published by the Banking Commissioner. Interest must be paid annually on the anniversary date of a tenancy either directly to tenants or as a credit towards the next month's rent.

The Department of Banking provides the rate at which interest must be paid.