In order to claim my grandmother on my taxes, do I have to go through my workplace or through turbo tax?

[Critter]

Your workplace has nothing to do with who you claim on an income tax return(an exemption)  ... the W-4 you fill in for work only adjusts the withholding amounts you have deducted at work (an allowance).  If you take too many allowances then you may owe at the end of the year.  Take to few and your refund increases ... it is a balancing act to get the bottom line you desire at the end of the year. 

[Carl]

Your workplace doesn't care who you do or do not claim on your tax return. If she actually qualifies as a dependent, you'll claim her as such on yuor tax return when you complete your tax return.

[VolvoGirl]

You add dependents to your tax return you file in April.  Is she married?  Does she live with you?  She has to have less than $4,200 income to claim her (not counting Social Security).

Who can I claim as a dependent?

https://ttlc.intuit.com/community/credits-and-deductions/help/who-can-i-claim-as-my-dependent/00/267...