A due process complaint is the formal request that starts an impartial hearing case.
What it says
It describes the child, the school, the problem (for example, services in the IEP that weren't provided), and what you're asking for, such as compensatory tutoring hours.
Where it goes
In New York City it's filed with the DOE's Impartial Hearing Office. Check the DOE's current instructions for how to file.
Time limits
Federal law generally gives two years from when the parent knew or should have known about the problem, with limited exceptions. Don't wait. Speak to an advocate or attorney about your dates.
What happens next
The district is generally expected to hold a resolution meeting before a hearing goes ahead. Read about that step.

