Why let Kate move back home when the killer is still out there?????

Just a question,

Why do the police allow Kate to move be back into her home knowing Casanova hasn't been caught yet??
I know they have finger prints etc & will know the killer soon but why Risk letting Kate return home (even with the cops on guard) it's really daft. She should stay in protective custody until the killer is either caught or dead!!

Also she's quite rude when she's talking to the killer (before she knows it's him) in her house

"You should use a collander, that will take you ages"
"What's taking my garbage out have to do with anything??"
"Rinse this off please"

If I were him, I'd say "oh I'm sorry boss lady" u can see where he's coming from telling Kate she needs to be broken down.
I'm not being daft, I'm all for strong women but she invited him in, don't boss him around!!

If it were me, I'd just allow my guest to sit down & talk to me whilst I chop the food, clean things off etc & I certainly wouldn't boss him around!