Part resident

It depends on more details. 

You only get a credit, for tax paid on double taxed income.

What are the two states?

What does "part resident" mean? Did you move during the tax year or do you have homes in both states? In the two homes situation, you are only a resident of one state. But the 2nd state might consider you a resident for tax purposes ("statutory resident"). In that case, you claim the credit on  your actual resident state return. 

The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you earned money in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state. You will have to file a non resident NY state return and pay NY tax on the income earned there..

What do you mean the program "always" does things?

There is no such thing as a part-resident of a state.  You can be a part-year resident of different states if you change your state of permanent residency, but permanent residency is indivisible and you can only be a permanent resident of one place at a time. 

You are only ever a permanent resident of one state at a time.  You are only a part-year resident of two different states if you move during the year (change your permanent residence).  This probably isn't happening every year.  It may be more likely that you are a permanent resident of state A and a temporary (non-resident) of state B.  In some cases, you may maintain a permanent home in state A, but live in state B for long enough that you are considered a "statutory resident" of state B, but that's different than being a permanent resident of 2 states at the same time.