Look carefully at the papers.
If the papers tell you to go to 250 Broadway, NYCHA is starting a termination of tenancy case through their administrative hearing process.
If the papers tell you to go to Housing Court, you are either being sued for nonpayment of rent or you have lost or defaulted on your termination hearing and NYCHA is bringing a holdover case against you. NYCHA will sometimes start a Holdover case without ever bringing a termination of tenancy hearing.