Should shared checking account be taxed when one of the account holders dies?

Question Details:

My mother recently passed away in PA. My sister had a joint checking account with my mother (her name "or" my sister's). My mother was in a nursing home for 8 1/2 years and all her SS checks were automatically deposited and then my sister would write a check to the nursing home, since my mother was on Medicaid. My sister closed this account and now is getting a letter from the state of PA asking for tax on half the account. We still need to get a headstone and other expenses on my mothers behalf. Shouldn't this money legally be my sister's with no tax?

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