Birth certificate in Japan help please

My daughter was born in Japan. She got a RFE to "submit a copy of the birth certificate showing the parentage which has been registered with the proper civil authortities of the country of your birth"

I am planning to submit the birth certificate from the Hospital. However, it seems like they need a formal one from the City Office.

Did anyone have similar experience? We have left Japan for several years.
I really have no idea what to do.
Please help!!!!!