I can certainly understand this is a frustrating situation for you. I suggest you contact an attorney to determine your legal options. You can find an attorney through the locator service on LawInfo’s home page at:
http://www.lawinfo.com/.
In many cases, permission for a guest to stay at your home can terminate at any time. However, there are cetain factors that may weigh in favor of whether someon is considered a guest or a "tenant" (tenants are entitled to proper notice to vacate). Important factors include those you described - whether rent is paid, whether there is a written lease, or even a verbal agreement regarding duration of stay, whether the person contributes to utilities or has duties around the house, etc.
Tenants may either be considered fixed term tenants (agreement for 6 months or 1 year, for example) or month-to-month tenants. Aside from any legally notice required to terminate a "tenancy," a notice period is typically recommended for guests to "keep the peace" so to speak regarding a move-out, particularly with somoene close like a family member. These situations can sometimes be sensitive - and I sense a bit of concern given that you think its possible she might not leave when asked. If a tenant does not leave when asked, then the landlord needs to formally evict the tenant through the court process.
You can also browse through the information in LawInfo’s Free Legal Resource Center here:
http://www.lawinfo.com/index.cfm/fus...lient.consumer, or search for your particular topic here:
http://resources.lawinfo.com/index.html.
See:
http://resources.lawinfo.com/en/Free...ado/index.html
http://resources.lawinfo.com/en/Lega...ant/index.html
See also:
Landlord Tenant Handbook published by the City of Fort Collins Neighborhood and Building Services:
http://fcgov.com/neighborhoodservice...lthandbook.pdf
http://www.courts.state.co.us/chs/co...s/fed/fed.html
http://www.dola.state.co.us/cdh/rese...s/tenant-l.htm