restraining orders are reserved mainly for domestic violence victims. so you would need to show that she has physically abused you or a member of your family. i dont think the fact that she is an addict and has stolen from you is going to do the trick - but
you can go to the court in your county and file for the RO - in your affidavit you will need to state that you are concerned for your wellbeing and the safety of your family - though you will need to cite specifics as to any attack or threats that she has made.
you will, unfortunately, need to file for eviction as the police stated - you cannot change the locks, etc until you do that - otherwise, she can take you to court and sue you - so the question you need to ask is does she have the knowledge and ability to do that if you take steps to bar her from your home without taking the proper steps.
to begin eviction proceedings you need to go to the court clerk and explain that you need the form to file for an eviction based on nuisance of this girl. here is a link for the CT courts that may be helpful to your to further understand the process and your rights.
i know this is a nightmare for you and i wish there were an easier way - unfortunately, no good deed goes unpunished. when you speak to the clerk, keep in mind, they cannot give you legal advice, but they can give you the forms and instructions. also, ask about having an eviction process put on the docket for an emergency hearing. that may be a possibility, too.