I'm on 20mg of celexa (citalopram) and have been taking melatonin over-the-counter to help me sleep. My wife said I should stop mixing these. Is it safe?

Probably safe. This is not a concerning combination and is probably quite safe. Caution should be advised when adding any sedatives, though, including alcohol or benzodiazepines.
Yes. As your depression improves, the sleep will also. This is a safe combination. To sleep restoratively is extremely important in order to improve depression.