B737-400 CAPT IGNORED THE NEED FOR AN ALTERNATE; IGNORED THE DISPATCHER ATTEMPT TO SUPPLY A LEGAL FLT RELEASE AND THEN OPERATED WITHOUT DISPATCH CONCURRENCE ON AN ILLEGAL FLT RELEASE.

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THE FLT MECH CALLED DISPATCH AT APPROX XA40Z WITH OUT AND PROJECTED OFF INFO FOR THE ACFT. DUE TO WX IN THE NE; I GOT THE RELEASE AND VERIFIED CURRENT WX FOR DEST AND ALTERNATE. THE TAF FOR THE ALTERNATE HAD BEEN REVISED AT XA13Z. I CALLED THE MECH BACK TO HAVE HIM ADVISE THE CAPT THAT A NEW ALTERNATE WAS REQUIRED. (THE ALTERNATE WAS AT 3/4 SM AND FORECAST WITH A TEMPO GROUP FOR THE SAME AT ETA.) THE MECH PASSED THE PHONE TO THE CAPT. I ADVISED THE CAPT OF THE CURRENT WX AND THE NEED FOR A NEW ALTERNATE. HE ASKED 'ZZZ1?' I TOLD HIM I DIDN'T THINK SO; BUT DIDN'T KNOW SINCE I HADN'T HAD TIME TO LOOK ANYTHING UP YET. I ASKED HIM TO GIVE ME 5 MINS TO WORK UP A NEW ALTERNATE WITH NUMBERS AND CURRENT WX. HE TOLD ME TO DO THE PAPERWORK SO IT LOOKED GOOD ON MY END AND HE WOULD GO WHEREVER HE COULD GET IN WHEN HE GOT UP THERE. I TOLD HIM HIS RELEASE WASN'T LEGAL AND HE NEEDED A NEW ALTERNATE. THE CAPT TOLD ME THEY HAD JUST BEEN DEICED WITH TYPE I; HAD TO GET GOING AND WOULD CALL ME ON THE PHONE LATER. I ASKED IF HE MEANT ACR X RADIO. HE SAID NO; THAT HIS ACFT HAD AIR PHONES. I VERIFIED HE WOULD BE CALLING FOR HIS NEW ALTERNATE. HE THEN TOLD ME HE 'DIDN'T HAVE TIME TO DEAL WITH THIS.' I ASKED HIM IF HE DIDN'T HAVE TIME FOR A NEW RELEASE AND HE HUNG UP ON ME. WHEN I CONTACTED THE FBO; THEY SAID HE WAS GONE AND COULDN'T GET IN CONTACT WITH THE ACFT; AND WHEN I CONTACTED THE TWR; HE HAD ALREADY TAKEN OFF. UPON REACHING HIS DEST; HE CALLED DISPATCH TO ASK FOR THE ALTERNATE AND MY INITIALS SO THE PAPERWORK WOULD LOOK GOOD AND I REFUSED.