This appears to be a misunderstanding. The box on the platform is for a battery, yes, but it was used to power an electric ignition coil:
The engine is geared to the wheel by means of a disk clutch. The flywheel, on the right side of the front wheel, contains a 6-volt lighting generator that originally furnished current for lighting and ignition, but the system later was altered by the addition of an ignition coil and four dry-cell batteries. The ignition switch is mounted on the right side of the frame, and the gasoline tank is above the front fender.
Pretty sure she is on a petrol one - there is a fuel tank above the front wheel, and you can see the fuel line going into the throttle body above the single piston engine. You can also see the exhaust and muffler below and behind the piston.
Also looking into it more, I don't think the Autoped was ever offered with an electric motor. Apparently the confusion comes from the fact that the company was bought out by the battery manufacturer Eveready, and sold as Eveready Autoped. Eveready modified the Autoped by adding a battery and ignition coil, replacing the original magneto system, but propulsion was always by means of a petrol engine.
I don't think the one in the photo has the battery and coil however - the coil can be seen here in front of the gas tank, but is missing in the OP photo.
I've been trying to find examples of the supposed marketing for electric cars where they were trying to promote it as a better choice for women because electric cars don't produce smog. I want to say "as if men wouldn't want less smog as well" but people roll coal going past me on the bike even here in canada.