Do I need a 50/60Hz notch filter for battery powered devices?
An ECG circuit picks up 60Hz "common mode" signal from both probes then inverts it and feeds it to the patient's foot to cancel it. The heart does not produce a common mode signal so its output is not affected by the common mode cancellation.
Here is the circuit:

 

(Image source: Analog Devices AD620A datasheet (old version))