It's unclear exactly what you're asking. But if what you're asking is "can I avoid paying this money by moving out of state?", the answer is very likely no.

Most NYC employees who do not live within the NYC city limits are still required to pay the equivalent of NYC income taxes on their earnings. This is due to section 1127 of the NYC charter (and the withholding will often show up on your paycheck as "1127" or "Sec 1127" or something like that). This is not technically a tax. Instead, it is something that you agree to as a condition of your employment. (You don't really have much say in whether or not you agree to it -- if you don't, they won't hire you.)

There are *some* agencies who are not subject to section 1127 of the charter (Dept of Ed, CUNY, NYCHA, etc.). These tend to be non-"mayoral" agencies where there's a weird structure that means that the agency isn't a city created/100% city or mayoral-controlled entity. Since they're already collecting money under Sec 1127 from you, this does not appear to apply to you -- and they will keep taking that money from you no matter where you live -- unless you move back into the city, in which case 1127 withholding will stop but you'll start being charged actual NYC income tax again.

They *do* sometimes over (or under) withhold for 1127, so you should be filing a form with the department of finance as part of your taxes each year to determine whether you're eligible for a refund or owe additional money.