Or is it Ms?
(Can you see what the difference is?)
|Mr. is an abbreviation for Mister.|
|Mrs. is an abbreviation for Mistress (not an adulterous woman).|
|Mr. doesn't identify marital status.|
|Miss identifies an unmarried woman.|
|Mrs. identifies a married woman or a widow.|
Ms. / Ms is not an abbreviation for anything.
So should you use a period at the end or not?
Since it's not an abbreviation you don't have to. However, it is also appropriate to add one if you wish.
The key here is consistency.
Pick one way of doing it and stick with it.
|That way people think you know what you're doing.|
Do you have a preference? Why?