Withholding for multiple states (NY and CT)

I read a bit and understand I won't be double taxed (resident of NY, working in CT).  However, what isn't clear after reading is if I actually need to have withholding for both states throughout the year?  e.g. Do I actually pay the taxes for both states, only to get a full refund from NY for my CT wages?  I don't understand why I should be required to have NY collect regular taxes from me (and hold on to my cash for a year) only to give it back to me on April 15 the following year.  What am I missing?  Let's assume the dividend / interest question is moot (I will pay estimated taxes on that in NY) and we are only talking state taxes on my wages.

 

Thanks!