I live in Overland Park, KS and have a house. I took a roommate in September. Her rent was $250 month. She paid the $125 for the first two weeks in February. I verbally told her not to pay the rest of February and that she could stay until the end of April and not pay rent, but that she needed to find something else. Since there was no lease agreement, do I need to do anything else? What happens if she has no place to go?

Strictly speaking you can't even begin to start eviction until the end of the period you told her she can stay, unless you choose to pretend you never said it since it's not in writing, not wise or fair. Not sure why you did that or why she stopped paying? Your best bet is to sit down with her, explain that you have to cover your bases legally, and give her written notice now for 30 days from now. After that you start eviction according to the laws of your state (tenant, or possibly lodger) at the court house that handles it near you, usually county.

You said she could stay until the end of April. So formalize that in a letter. If she has failed to leave at the end of April, then May 1 you file for an eviction order.