Ask your landlord to let you see it at the beginning of the rate period. Tell him you think your refrigerator is using too much electricity and you want to track it. Let him/her see you write down the reading from the meter. Tell them you'll want to see it again in 30 days. This may scare them enough to disconnect. 

You'll know if your next bill has a noticeable drop. In a couple of months, if it goes up again, ask the electric company to check it. Let them catch him. Keep in mind, if you're wrong you're going to pay for their visit.