One of the first things you should know is that it is illegal in many states to ask someone if they are in a relationship during the interview process. If this is the case (or even if it isn't and you simply don't want to know the details), you can always ask if there will likely be someone staying in the apartment with them for a certain amount of time. Explain that anyone who stays more than three or four nights a week (or month) is considered a tenant by your lease and must be screened as well. This can help prevent you from finding out that there have been two people living in the place when you were under the impression that there would only be one.
This is something that should be backed up by your lease. Include a clause that states that anyone found to be living in the apartment for a certain amount of days per month is also considered a tenant and will also have to pay rent. You may even want to explain that this may be terms for termination of the lease. At the end of the day, it is up to you how you feel like handling this situation but you want to be able to have all of your bases covered. You certainly don't want to be caught off guard with a squatter of any kind.