You don't need to hire an attorney when you rent a house or apartment in Mexico, but it wouldn't hurt to have the rental contract signed in front of an attorney, better if it's a "notario público" (notary public). A notario público in Mexico is a lawyer who deals with land and real property buying and selling or renting. The notario público will make sure that the contract is valid. If there's any problem down the line, he'll back it up and be there to assist you.
However, if you're renting from somebody who has a good reputation, you don't have to sign the contract in front of a notario público and the contract signing can just be between the landlord and renter.
(Bedroom at Hotel Perico, Lake Chapala, Mexico, pictured.)