My mother passed away January 2016 can I still claim her as a dependent in my 2016 tax return

[Phillip1]

Yes. You can claim a dependent who died during the year if you would have been entitled to claim their exemption if they would have survived through the end of the year.

See this explanation from IRS Publication 501:

Death or birth. A person who died during the year, but lived with you as a member of your household until death, will meet this test. The same is true for a child who was born during the year and lived with you as a member of your household for the rest of the year. The test is also met if a child lived with you as a member of your household except for any required hospital stay following birth.

 If your dependent died during the year and you otherwise qualify to claim an exemption for the dependent, you can still claim the exemption.

[Marty2013Rocky2013]

My mom passed in 2021

[Marty2013Rocky2013]

My mom passed away September 8,2021. Can I claim her as a dependent on my 2021 taxes?

[SweetieJean]

Yes, if she otherwise qualified.