If you don't mind a guesstimate, I'd say 1977 or 1978.
Follow-up: I checked the N-frame serial number listing in "Standard Catalog of Smith & Wesson." Serial numbers N190001 to N430000 were manufactured from 1975 to 1977. So 1977 as the manufacturing date for N367XXX sounds about right. I hope this helps.
[This message has been edited by jimmy (edited April 20, 1999).]