Oswald's autopsy was conducted in Dallas by coroner Earl Rose.
The Secret Service took custody of JFK's body because they wanted to
get the new president and the rest of the entourage out of Dallas,
where their lives could be in danger (no one knew yet if the shooting
was the work of one individual or a larger plot), and Mrs. Kennedy
refused to leave Parkland Hospital without her husband's body.
(William Manchester's DEATH OF A PRESIDENT has a detailed account of
the incident.)
When it came to Oswald's autopsy, there existed no such emergency.
Dave