Yes, you should use the preposition "in" here. However, there is also a very formal rule regarding prepositions that we really only follow when writing academically or in extremely formal situations. One of the unspoken grammar rules of English is "never end a sentence with a preposition". However, almost nobody follows that rule in daily spoken English. So, for EXTREMELY formal English, write this. "In which state do you live?" In normal, every-day English, just put the preposition at the end. We don't care about that formality.

Hi Jasmine! Yes it is appropriate to use "in" when asking about a place. Their response would then be "I live in the state of Washington" for example.

Yes, that is correct.