Can I claim my daughter who lived with me for more than half the year on my federal but not NY state return for eic?

You may claim your daughter as a dependent on your 2016 income tax return if all of the conditions to the IRS test below have been met: 

A parent may claim their child if they meet either the qualifying child or qualifying relative test as outlined below:

Qualifying Child

These 5 tests (all of them), will qualify a child as a dependent:

• Relationship: They must be your child, adopted child, foster-child, brother or sister, or a descendant of one of these (grand or nephew).
• Residence: They had to live with you in the same residence for more than half the year. Being away at school is considered as living at home. 
• Age: Must be under age 19 or under 24 and a full-time student for at least 5 months of the year. They can be any age if they are totally and permanently disabled.
• Support: child did not provide more than half of their own support during the year.
• Joint Support: The child cannot file a joint return for the year.

So, if you meet all of the above conditions, you may claim your daughter as your dependent on both the federal and New York State tax returns. I have included a Link with information for your NYS tax return.  I didn't see anything that prohibited a taxpayer from not claiming someone as a dependent.

https://www.tax.ny.gov/e-services/training/preparer/pdf/Dependent%20Exemptions.pdf