The general's father, H. Norman Schwarzkopf Sr., was a career Army man who was appointed to organize the New Jersey State Police in 1921 and was its commander until 1936. That put him smack dab in the middle of investigating the kidnapping and murder of Charles Lindbergh's baby in 1932, and he testified in the trial of Richard Hauptmann, who was later executed for the crime, although questions about his guilt remain.
Well, almost. I did some googling and found that the connection to Elisabeth Schwarzkopf was indeed an urban myth, even though it was presented as fact in some obituaries when she died in 2006.
Elisabeth was an only child, so of course she didn't have any nieces or nephews. And her family was as firmly ensconced in middle-class Germany as the Norman Schwarzkopfs were in New Jersey. Norman Sr. was born in Newark in 1895, 20 years before Elisabeth's birth in Poland, and Norman Jr. was born in Trenton in 1934, in the middle of his daddy's biggest case.