Do you think she is asking me to stay at her house on friendly terms or more?

She had a breakup about a month ago and we went out together after that happened, we've gotten closer since then, barely knew each other before, but I'm still unsure where we stand

She literally told me one of the issues with her ex was he didn't like to sleep in her bed with her cats also so he would often just go to the couch or she'd go at times with her cats, and that "what was even the point of staying over if we're not gonna sleep in the same bed"

That same night we went out she asked me if I wanted to stay over and I politely declined because of work, but really because I barely know her and she had just had a breakup. I do feel like she became a little distant after that night but we still talk and flirt and hangout a bit. Now this week my apartment was being fumigated and she told me I could stay at her place. Since I'm still unsure about where her head is at I said thank you and I'll think about it. She said at least twice "you let me know.."

She's very touchy with me at times, this week in particular "scaring" me from behind by poking me but at other times becomes very distant randomly. This week was mostly positive, even heard her talking to a friend about how I always mess with her, and giving huge smiles when I saw her. She constantly comes to talk to me during a very long cooking class we have, and at times hang out afterwards, usually at her house to smoke before work. But I've asked her to lunch a couple of times before this week and she either cancels or says she can't. I just don't know what to make of her and if I should make a move on her or not

Do you think she is asking me to stay at her house on friendly terms or more?
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