Do I need a NOC for a passport if my father is a government employee?

No. You dont require an NOC.

Only your father require NOC while applying for Passport. For issuance of a fresh passport, Government/Public Sector/Statutory body employees need to submit either Identity Certificate in original as per Annexure "A" or No Objection Certificate (NOC) as per Annexure "G" or Prior Intimation Letter (PI) as per Annexure "H" as an additional document along with the application form. If he/she submits Annexure "A", passport will be issued without police verification and if he/she submits Annexure "G", passport will be issued on post police verification basis and if he/she submits Annexure "H", passport will be issued on pre police verification basis. For re-issue of passport, Government/Public Sector/Statutory body employees need to submit No Objection Certificate (NOC) as per Annexure "G" or Prior Intimation Letter (PI) as per Annexure "H" as an additional document along with the application form.

You dont require an NOC for applying for Passport.

However, if you are a minor and your father is a government emplyee, you need to submit Annexure A.

Annexure A is an Identity Certificate required to produced by all central government employees, state government employees, employees of statutory bodies and public sector undertakings, their spouse and children upto the age of 18 years.