While there does not appear to be any reference on Form 1040 U.S. Individual Income Tax Return nor in the IRS instructions requiring a Social Security Number (SSN) be entered for the qualifying child when a return's filing status is Head of Household (HoH), the IRS does have a rejection code that will reject any return e-filed that does not contain an SSN for a qualifying child for HoH purposes. Due to this rejection code, the only way to file a return without an SSN for the qualifying child would be to paper file the return.

Note that any link in the information above is updated each year automatically and will take you to the most recent version of the webpage or document at the time it is accessed.