A two digit date is on the counterweight of the crankshaft if you're ever in that deep. It is usually within a year of the saw's production date. Oddly, some silver tagged 61's and 266's also have a four digit year stamped on the tags - don't know why that approach was only used on some.
According to a serial number-to-date cross reference sheet I have, that saw was produced sometime after Jan 1981 but the sheet stops at 1981 so I can't get it any closer. But likely an '81 or '82.