Can I claim my disabled sister as a dependent on my taxes if she does not live with me but the state pays me to take care of her?

You can only claim your sister as a Dependent if you pay for more than half of her needs [shelter, food, clothing, medical, etc] from your own pocket with money earned not from Medicaid as being her Caregiver.

The taxpayers are already paying you a salary from the Federal/State government, so it wouldn't be fair to also take your sister as a Dependent on your Federal/State income taxes.

No you cannot. She is living in a group home under Medicaid? Who do you think is paying for that?

Also remember that if she is on Medicaid you claiming her as dependent can really mess up Medicaid.

Your profile states that you're caring for someone living in an independent living facility. Are you paying for her care at the IL facility? What care are you providing yourself? The IRS has very specific criteria for claiming a dependent. You can research its website and locate those criteria to see if you meet them.