My mom is in a NH in ME. What assets can the state take to pay for it?

The state won't take her assets. Instead, she will not qualify for state aid until she uses nearly all her assets on her own care. One car and a house are exempt, but the state can claim proceeds from the sale of the house after she dies, to repay them what they spent on her.

Generally applying for Medicaid for a single individual is pretty straight-forward (compared to when a couple is involved). But if there are a lot of assets or complex ownership questions, it would be good to consult an attorney who specializes in Elder Law.