German birth certificates/records from 1960-1963?

My father was born in 1961 in Munich, Germany; however, his mom refused to discuss who his true father is and we don't have a live birth certificate... He was later "adopted" by the man she married after my dad was born. He was stationed in Germany, they got married, and when my dad was around 3-5 years old, they moved to America. Does anyone have an idea how to access public records like that or maybe another idea? I would love to know my true blood heritage.