A VERY LOW TIME PLT; CLRED FOR LNDG AT CHD; WAS TWICE CUT OFF BY A TWIN COMANCHE. HE RPTED AN NMAC WITH PRESCOTT FSS.

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UPON RETURNING TO LAND AT CHD; I RADIOED THE CTL TWR AND ADVISED THAT I WAS OVER MEMORIAL AIRFIELD (L07) AND INBOUND FOR A TOUCH-AND-GO LNDG. THE CTLR ACKNOWLEDGED MY REQUEST AND DIRECTED ME TO MAKE R TFC FOR RWY 22R AND TO RPT ENTERING THE DOWNWIND. JUST PRIOR TO REACHING THE DOWNWIND LEG; I NOTICED A PIPER TWIN COMANCHE THAT APPEARED TO BE APCHING (OR ALREADY ON) A L DOWNWIND FOR RWY 4L. THE TWIN COMANCHE WAS AT MY APPROX ALT (2200 FT MSL) AND APPEARED TO BE TRAVELING AT AN UNREASONABLY HIGH RATE OF SPD. THE 2 ACFT WERE SEPARATED BY LESS THAN 100 FT VERTLY AND BY LESS THAN 3000 FT LATERALLY. WHEN THE TWR CTLR REQUESTED THAT I RPT MY POS; I REPLIED THAT I HAD JUST ENTERED A R DOWNWIND FOR RWY 22R AND THAT I HAD BEEN CUT OFF BY THE TWIN COMANCHE. THE TWR CTLR THEN ADVISED THE TWIN COMANCHE PLT THAT HE WAS NOT IN THE CORRECT TFC PATTERN; AND TO ENTER THE CORRECT PATTERN IMMEDIATELY. JUST PRIOR TO TURNING BASE FOR RWY 22R (AND WITH A CLRNC TO LAND ON RWY 22R); I OBSERVED THE TWIN COMANCHE PASS UNDERNEATH MY ACFT AT AN UNREASONABLY HIGH RATE OF SPD. THE 2 ACFT WERE SEPARATED BY LESS THAN 100 FT VERTLY AND BY LESS THAN 50 FT LATERALLY. I IMMEDIATELY TOOK EVASIVE ACTION TO AVOID COLLIDING WITH THE TWIN COMANCHE. UPON OBSERVING THIS; THE TWR CTLR CANCELED MY LNDG CLRNC AND CLRED THE TWIN COMANCHE TO LAND AHEAD OF ME. THE REMAINDER OF MY FLT WAS COMPLETED WITHOUT INCIDENT. UPON RETURNING HOME AFTER THE FLT; I CALLED THE CHD TWR AND REQUESTED THE REGISTRATION NUMBER OF THE TWIN COMANCHE. I RECEIVED THAT INFO; AND WAS ADVISED THAT THE PLT OF THE TWIN COMANCHE HAD BEEN INSTRUCTED TO 'CALL THE TWR' UPON LNDG. I LATER FILED AN NMAC RPT WITH THE PRESCOTT FSS.