If you are a Connecticut resident, you do not have to file a nonresident New York State return or allocate any wages to NYS. Nonresidents are liable to report income and pay tax on compensation for services performed in state. Even though your patients live in New York, you are actually performing services in the state of Connecticut.
Per NYS, days worked at home are considered New York work days only if the employee’s assigned or primary work location is at an established office or other bona fide place of business of the employer (a bona fide employer office) in New York State. If the employee’s assigned or primary work location is at an established office or other bona fide place of business of the employer outside New York State, then any normal work day worked at home would be treated as a day worked outside New York State.
For more information, please see Instructions for Form IT-203.