Surprisingly, the answer is, maybe.
The first big eye opener is that CT has law which makes children responsible for their parent's care, until the parent reaches age 65. CGS Sec. 53-304. Not only can they make you pay, they can imprison you for a year.
Fortunately for us, this law is rarely enforced.
Second, people often do planning or transfer assets late in life to preserve some assets for their family and qualify for Medicaid. CT recently passed a statute that allows the nursing home to go after assets that were transferred within 2 years of entering the nursing home. CGS Sec. 17b-261.
In addition, the contract you sign with a nursing home will often have provisions allowing recoupment of money. Read it carefully.
So yes, you may have to pay for Mom's nursing home.