Depends on which Colt. The colt police positive .38 & bankers special with serial # 329802 was produced in 1930. The colt police positive special & detective special with serial # 329802 was produced in 1926.
The serial number you give is too low to be a Colt detective special. Colt detective specials were produced in 1927 starting with serial number 331000.They were cut-down versions of the Colt police positive specials. Now the Colt police positive special with that serial number was made in 1912.
Police positive heavy frame: 1925 starts with Serial # 250000. Police positive special & Detective special: 1908 starts with Serial # 1 Police positive .32 & target: 1907 starts with Serial #495000 Police positive .38 & banker's special: 1905 starts with Serial # 1