Others Claiming Me as Dependent: Do My Changes Apply Both to Federal and State Returns

[FleekerCD]

My federal and state taxes were rejected because I mistakenly selected "no" to the question of whether others could claim me as a dependent. (My parents can do so.) 

So I fixed that setting in my personal information in Turbotax, and this fixed the federal return.

However, I cannot see an area on my New York State return within Turbotax where I can even check on this question. 
My question is this: If I fixed the setting in Turbotax, does the software then apply that both to federal and state returns on its own?

[KeshaH]

If needed on the state return, this information flows from the federal. It's likely your state return was rejected simply because your federal return was rejected and not for any specific reason. Many state returns automatically reject if the federal return gets rejected. You should be good to resubmit your return with the change you made.