You may be eligible to claim both your niece and her son as dependents on your return. In order to claim someone as your dependent, the person must meet certain tests as shown below.
The dependent must be:
- Either your qualifying child or qualifying relative
- A U.S. citizen, U.S. resident, U.S. national or a resident of Canada or Mexico
- Unmarried or, if married, not filing a joint return or only filing a joint return to claim a refund of income tax withheld or estimated tax paid.
Additionally, you must meet the dependent taxpayer test. If you can be claimed as a dependent by another person, you can't claim anyone else as a dependent.
The requirements for qualifying child and qualifying relative as well as additional information regarding these tests can be found in Publication 501, Dependents, Standard Deduction and Filing Information.