It does not necessarily indicate a problem. If the cooling system was over filled while cold, the excess will have to escape from the overflow when the pressure builds. This is normal. If it continues after several periods of the engine warming up, it may mean that the cap is defective.
bad hose, radiator leak, leaking into engine.
Water Leak upper or lower hose Water Pump Failure Thermostat Stuck in Closed Position Blown Head Gasket Fit new radiator cap
If your 1997 Subaru Legacy is the same as My RS-B Twin Turbo?, the Radiator and Overflow bottle have to come out and the Thermostat is at the front of the Engine, down the bottom-just to the right of centre, (Thermostat is inside the bottom radiator hose), - My Thermostat just twisted/pulled out, let all old coolant flush out-put New Thermostat in its place, Radiator and Overflow bottle were put back in and radiator topped up with fresh coolant and water, Overflow was filled to second line as it should be, car was started with heater on full for 5 minutes to disperse any air in water - (note) after adding fresh coolant, add water in Radiator till it can't take anymore-to show its filled properly.
Have you pressure tested to rule out a blown head gasket? Does the cooling system build up full pressure and start dribbling into the overflow long before the engine is hot? If so, it could be exhaust gas leaking into the cooling system.
Should be a plug at the bottom or rear of radiator
The radiator
yes it could be faulty without leaking , the impellor on the back could of come away and not be pumping water around the engine , to check this take the radiator cap off and have a look if the water goes up and down when you excellorate the engine , if it does the must be a nother problem
bottom radiator hose
On the top left hand side of the radiator there is a square screw-in plug with a Philips head. Take it out while filling the radiator to let the trapped air out.
Yes it could be failing, but read on.Crawl under vehicle and observe water pump area(where lower radiator hose attaches). There is a weep hole on back of pump. If there is coolant or traces of coolant residue. Suspct failing water pump or excessive pressure causing leakage. Excessive pressure can be caused by failing headgasket or gaskets. If overflow reservoir is slimy and dark,and overfull suspect headgasket.
Coolant always goes in the top of the radiator.
The radiator should be the same for all 95-99 model year Subaru Legacys. If I remember correctly, the upper and lower radiator hoses can be different, though, depending on the engine (i.e. EJ22 vs. EJ25) or Legacy version (i.e. Outback, etc.).