Grace periods as they pertain to rent or any other financial obligation must be written into the contract. Check your lease to see if there is an alloted grace period.
The only grace period allowed to a renter are those specified in your rental contract. For example, if the contract states one month free rent, then they must give you that grace period.
You should read your lease over very carefully. If there is a grace period, it will be explained in the lease. I don't believe there are state laws that give a specific grace period. It's determined by what you agree upon with the landlord when you sign your lease agreement.