As I stated in my post earlier if the laws there are similiar to the ones here there does not have to be a specific arrangement for payment just an agreement to let her stay there (and not just yeah sure spend the night or the weekend). There is also no specific time period here (like the 30 days) but obviously the longer the person is there the more it goes to show that they reside there. If you agree to let a friend stay with you for a couple nights then they dont leave that is one thing but if it is weeks or an undetermined amount of time you are SOL as far as the police are concerened. The police, at least no officer here, would touch this situation with a ten foot pole, it is a civil matter, it is not Criminal Trespass by our statute, it is a civil dispute over what the agreement was and we have no authority to physically remove someone form the residence absent any criminal law violation.
Always have a written agreement and even then you might find yourself having to actually get a cort order to get them out. We get calls all the time from landlords that have gone through the eviction process and want someone removed but if the tenant is stubborn and refuses we can not act until they get that final court order that authorizes law enforcement to physically remove them. It is basically a three step process, a landlord issued eviction, a court issued eviction, and then the final "get out now (usually 10 day notice) or the police will come help you out" notice.
As TJR stated she was a tenant under the law not just a guest in the home. Again I'm glad it worked out for you. There are generally ways to make it work out because most people do not want to stay in a house where they are not welcome, at least not in the same house with the owner, when it comes to a rented house many tenants will stay there until the very last second because until the moment they move out they have the control and privacy and the landlord is just waiting to get the process complete.
