Well, according to a thread here, entitled "Three Purple Hearts and Early Discharge for John Kerry, the Walking Wounded" "After his third Purple Heart Kerry requested to be sent home. Navy rules, he pointed out, allowed a thrice-wounded soldier to return to the US immediately. Commodore Charles F. Horne, an administrative official and commander of the coastal squadron in which Kerry served, filled out a document on 3/17/69, that said Kerry had "been thrice wounded in action while on duty incountry Vietnam. Reassignment is requested...as a personal aide in Boston, New York or Wash. D.C. area". This says he was reassigned, notwithstanding the title of the thread.
And Douglas Brinkley says in his book "It was during Kerry's second tour of duty in Vietnam in late 1968 and early 1969 that he encountered the gravest danger as he commanded his boat up dark waterways lined by jungles infested with Viet Cong snipers.
After being wounded for the third time, Kerry asked to be transferred stateside and took a desk job in Brooklyn, NY."
http://www.chron.com/cs/CDA/ssistory.mlp/nation/2402160 I haven't seen anything that says he was discharged, only reassigned.
Kerry didn't even finish that statewide assignment:
John Kerry did not complete his tour of duty in Vietnam – he opted out; he cut and ran. In March of 1969, despite the fact that he was not disabled in any way, John Kerry appealed to Commodore Charles F. Horne for an early transfer out of combat. His request was granted on March 17, 1968. A loophole in the rules permits a soldier who has been “thrice wounded” to request transfer out of combat. Although Kerry’s wounds had been nothing more than band-aid “boo boos”, and he was perfectly fit to serve, Kerry explicitly declined to continue serving his country. Kerry, for lack of a better phrase, opted to cut-and-run.
Kerry ended up with a cushy desk job in Boston, working for Rear Admiral Walter F. Schlech, Jr.
But Kerry found even that to be too onerous, getting in the way of his political ambitions. Thus, on January 3, 1970, Kerry requested a complete discharge from the service – so he could run for Congress. Kerry’s request was granted, though he dropped out of the race only three months into the campaign.
http://www.boston.com/globe/nation/packages/kerry/061603.shtml