Uhm, OK, I'll rephrase that. In the US, FAR 121.359 says..
(a) No certificate holder may operate a large turbine engine powered airplane or a large pressurized airplane with four reciprocating engines unless an approved cockpit voice recorder is installed in that airplane and is operated continuously from the start of the use of the checklist (before starting engines for the purpose of flight), to completion of the final checklist at the termination of the flight.
The only 737-300 checklist I can get my hands on says nothing about manually activating the CVR so I have to believe that models meant for US airlines have the CVR start with basic aircraft power up. Boeing custom builds each model per the airlines request so your mileage may vary.