Coleen, then why does NYS non-resident form IT-203 use dividend income and interest income to compute NY taxable income on line 36?

Many states have an adjustment section, where you can remove a state's income that doesn't belong. If that is not available, you can delete the interest and dividends, delete NY state, redo NY state and enter the interest and dividends after NY state is completely done.

No. You only report it to your home state.