Noisy neighbors feuding...

Downstairs tenant complained about loud noises all thru the night. Spoke to upstairs and they denied any inappropriate noise and reported that it is actually the downstairs tenants that are inappropriately loud. They are now going back and forth complaining (letters in the drop box and along with their rents and stopping by the office) about one another & insisting I fix it. How do I determine the guilty party and how to I end this feud? Downstairs has now taken to posting notes on upstairs' mailbox, cars, & door. I don't know how to remedy this short of sitting outside their apartments and confirming noise levels... I know I need to do something but I would hate to evict someone without all the facts. No other neighbor has complained at all.