How do I change my household SSN on my state return

Perhaps you'd better (fully) explain what you are trying to do, and where you live (state).   There is no such thing as a "... household SSN ..." (perhaps maybe an address).

 

Only people (and each person living in your house) have SSNs.

 

 

You would need to revisit the personal section under My Info in the program.

 

In TurboTax online,

 

• Sign in to your account, select Pick up where you left off
• To your left, select My Info
• On the screen, Personal Info Summary, scroll down to edit 
• The information will be carried over to the state tax forms