Ma, this woman keeps following me home, may I keep her, please?

No, son.
You can politely escort her to her home, and then, at the front door and without entering, ask her whether she'd like to get to know you better. If she says yes, make a date.

Only if you promise to take care of her.  Keeping a woman is a big responsibility.  You'll have to fed her, brush her, and make sure she gets plenty of exercise.  She can sleep on your bed sometimes, but for the most part, she’ll have to stay in the kitchen or go outside.  Ok?

What else are you hiding?

if u and her are single yes u can let her stay at ur house