Of course there is.

https://doccs.ny.gov/file-complaint

> Incarcerated Individuals can contact OSI directly by dialing 444 from any incarcerated individual phone Monday through Friday between the hours of 8:00 am and 5:00 pm.

https://www.ojp.gov/ncjrs/virtual-library/abstracts/inmate-g...

> Every jail must develop a clear and responsive prisoner grievance procedure, including a formal means of delivering complaints and concerns from a prisoner to the administration and the procedures by which the prisoner receives a written response. However, the prisoner should not be able to use the procedures to avoid institutional rules and regulations.