T-6 HAS NMAC WITH TWIN.

Narrative

I DEPARTED SOUTH ST PAUL ARPT (D97-FLEMING FIELD) AND CONTACTED ST PAUL DOWNTOWN ARPT (STP-HOLMAN FIELD) TWR REQUESTING TO DO 2 TOUCH AND GO LNDGS. I WAS CLRED TO DO SO USING R TFC FOR RWY 32. AFTER THE SECOND LNDG; I ASKED TO DEPART THE PATTERN TO THE E. I WAS CLRED AS REQUESTED AND FLEW ON A 90 DEG HDG FOR APPROX 4-5 NM; AND THEN HEADED SW TO RETURN TO FLEMING FIELD. APPROX 2 NM NE OF FLEMING FIELD AND AT 2000 FT MSL; I NOTICED A TWIN ENG ACFT APPROX 2 NM AWAY AT MY 10 O'CLOCK POS. AT THAT TIME THE OTHER ACFT WAS ABOVE MY ALT; BUT IT WAS APPARENT THAT HE WAS DSNDING ON THE GLIDEPATH TO RWY 32 AT HOLMAN FIELD. I DSNDED TO 1800 FT MSL; PASSING UNDERNEATH AND AHEAD OF THE OTHER ACFT BY WHAT I WOULD ESTIMATE AS 500 FT. IMMEDIATELY AFTER WE CROSSED PATHS; THE PLT OF THE TWIN RPTED SEEING US TO THE HOLMAN FIELD TWR. THE TWR OPERATOR WAS UNAWARE OF OUR POS AND DID NOT REALIZE THAT THERE WAS A POTENTIAL TFC CONFLICT. I TALKED TO THE TWR OPERATOR AFTER LNDG AND SHE SAID THAT SHE WAS UNAWARE THAT I WAS RETURNING TO FLEMING FIELD. IN RETROSPECT; ALTHOUGH I WAS OUTSIDE OF CTLED AIRSPACE; HAD I INFORMED THE TWR OPERATOR OF MY INTENTIONS TO RETURN TO FLEMING FIELD; SHE WOULD HAVE BEEN ABLE TO ADVISE BOTH THE TWIN ENG ACFT AND MYSELF OF THE POTENTIAL TFC CONFLICT.