When you live in an apartment without a lease you are considered an "at-will" tenant. You still have rights, however. The law varies from state to state. Renters' rights in Minnesota without a lease protect both the renter and the landlord against unethical behavior.
In Minnesota, anyone who rents a domicile has a lease. What's known as an "at-will" tenancy in other states is called a "periodic lease" in Minnesota. This is a rental agreement with no definite end date. The rental agreement is renewed every time rent is paid unless one or both parties terminate the agreement. You must provide notice of at least the length of the rental period to terminate a lease.
Your landlord has the right to require a security deposit. There is no limit to what your landlord can charge you for a security deposit. State law allows landlords to increase the amount required for a security deposit at any point during a periodic tenancy. However, the landlord must provide you with notice before increasing the deposit. The law requires that your landlord give you notice of at least one rental period.
The landlord is required to provide you with a livable apartment. He must make all repairs required to keep the building up to code. You have a right to doors that lock, heat, electricity and running water. Your landlord must respond to any maintenance requests; failing to act is a violation of state law. You should contact the fair housing department.
Your landlord must provide you with notice, even if he evicts you. Your landlord will file a suit in tenant court. She then has seven days after filing to have someone else serve you with papers telling you when to appear in court. Your landlord cannot forcibly evict you, either by throwing your things on the street or by making your apartment uncomfortable. He might try do the latter by removing locks or shutting off utilities.