Tax Year Prior to 2020: My niece is my dependent, can I claim her?

Yes, as long as your sister isn't claiming her. And that depends on when last summer, your sister moved out. It's not clear if your niece is still living with you or she moved to TX with her mother.

There are two types of dependents, "Qualifying Children"(QC) and other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and residency requirement. Only a QC qualifies you for the Earned Income Credit and child tax credit. They are interrelated  but the rules are different for each.

A child closely related to a taxpayer can  be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:

1.                   He is under age 19, or under 24 if a full time student for at least 5 months of the year, or  is totally & permanently disabled

2.                   He did not provide more than 1/2 his own support

3.                   He lived with the relative (including temporary absences) for more than half the year

4.                   He is younger than the relative (not applicable for a disabled child)

5.                   If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child (this essentially means that you have the parent’s permission to claim the child). So, if your sister also lived with her child for more than half the year, she has first claim on the dependent, regardless of who provided the support.

6.                   If the parents of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child. 

Yes, you can claim your dependent child on your return if you answer all to the following:

Are they related to you? 

Do they meet the age requirement? They must be under the age of 19 or, if a full time-student, under the age of 24. There is no age limit if your child is permanently and totally disabled.

Do they live with you? They must live with you for more than 1/2 of the year.

 Do you financially support them? Your child may have a job and earn income, but that job cannot provide for more than 1/2 of their support. You need to be providing for more than 1/2 of their support even while they are working. 

Are you the only person claiming them? If you and your spouse are divorced, you need to be the one claiming them for tax purposes. 

Turbotax will guide you through a series of questions under the Personal Information Tab.