Rossbach was born in Newark, New Jersey in 1903, the son of Adam J. and Rhoda Rossbach. He attended Colgate University, graduating in 1925, and South Jersey Law School (now Rutgers School of Law–Camden), graduating in 1932. He was admitted to the New Jersey bar in 1935 and joined his father's law practice. He was made partner in Rossbach & Rossbach in 1936.
In 1942, he was named Assistant U.S. Attorney for the District of New Jersey. He was promoted to U.S. Attorney in September 1945 following the resignation of Thorn Lord. Among the figures prosecuted during Rossbach's tenure were labor leader Joseph S. Fay, charged with income tax evasion, and former New Jersey Attorney General Walter D. Van Riper, charged in a check kiting scheme. Both Fay and Van Riper were subsequently acquitted. He resigned from office in May 1948.
| United States Attorney for the District of New Jersey
1945 – 1948