If you live and work in NY and never physically work within Ohio, you do not have to file a tax return in Ohio. Your income is fully taxable by your home state of NY.
A few states tax non-resident remote workers, but Ohio is not one of them.
Be sure you company's pay roll doesn't try to withhold Ohio state or city income tax. You can get it refunded, but will have the hassle of filing returns. In particular, employers frequently (and mistakenly) withhold city tax because their HQ is in that city. As a remote worker, you are not subject to OH city income tax unless you physically work in the city
Does that answer apply to me too?
I live and work in NY -- but my employer is located in PA.
Unfortunately, despite my protests, my employer has been withholding PA state income tax from my pay.
Is there a way for me to get them to stop doing that (besides asking them)?
@greenfa Your situation may be different.
Telecommuting. If you work outside the state as a job requirement, you are only subject to PA income tax on the days you work in PA. But if you work outside PA for your own convenience, you are subject to PA State income tax on all your income. NY, Nebraska, Delaware and New Jersey have the same rule. For guidance see: http://www.journalofaccountancy.com/issues/2009/jun/20091371.html
@greenfa -- Here is PA's "Convenience of the Employer" rule, spelled out in detail:
Pennsylvania, like many other states, follows the “convenience-of-the-employer” doctrine. It provides that compensation for services performed by nonresidents cannot be allocated to the services’ actual places of performance if they were performed there only for the employee’s convenience or if they were not performed there “of necessity in the service of the employer”. In these instances, the compensation must be allocated only to the state (or among the states) where the employee is of necessity performing actual services in the service, and for the convenience, of the employer.
The only factors considered under this doctrine are:
Whether the services performed by an individual outside the taxing jurisdiction were performed in the service, and for the benefit, of the individual’s employer; and
Whether such services were such that they could have been performed at an office of the employer within the taxing jurisdiction (or could have been performed at an office of the employer within the taxing jurisdiction had the employer made suitable accommodations available to the employee).
Consequently, under the “convenience-of-the-employer” doctrine, allocation depends upon whether the services in question are of a character required to be performed away from an office of the employer and outside the taxing jurisdiction or require highly specialized facilities not available at or near an office of the employer. https://www.revenue.pa.gov/FormsandPublications/PAPersonalIncomeTaxGuide/Pages/Gross-Compensation.aspx#Nonres-AllocPAComp
So if you were working outside of PA "of necessity in the service of the employer", your income would not be subject to PA withholding or PA income tax. If that's your situation, you should submit PA Form REV-419 to your employer. Here's a link to that form: https://www.revenue.pa.gov/FormsandPublications/FormsforBusinesses/EmployerWithholding/Documents/rev-419.pdf