Get your taxes done using TurboTax

....if you mean that whatever you get from the Child Tax Credit, or EIC on your own tax return....and it is those $$ you put into a 529 account for the child.....then, yes, you would need to discuss that with the other parent about how those particular $$ are to be handled before you change your procedures, because one, or both of those credits will show up on his tax return if you switch.

......( assuming that the other parent in this houshold can leagally include the child on his tax return).... if you truly trust your significant other to give you back those to put into the child's 529 account, or puts them there directly himself, then it shouldn't make too much differnece.   But, you would both have to test prepare each of your 2016 tax returns both ways to see if there truly is any advantaage to switching.    So much depends on exactly how much each of you earns, that we can't really tell you which way is most advantageous for your situation.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*