Schematics are linked on its project page, they show direct connection between the input and output on one rail.
The thing with oscilloscopes is, all GNDs are connected and permanently connected to earth over its mains input (if it has one and does not run on battery or is not connected to earth in any other way).
The µCurrent is a battery powered device and itself floating in regards to earth, as long as you keep it isolated. But once you connect oscilloscope GND to be able to see a signal, you ground that point in the circuit to earth. Think twice and measure if you work with non-isolated power supplies and such, it might be irrelevant if the power supply of your circuit is isolated or battery powered. It might also make sense to take chargers into consideration if it´s a device with a charger. You should safely measure these things before making a connection.
Every time you need to measure between points of which both are not connected to earth, you need a differential probe that is isolated. Some people make the scope floating by isolating its earth connection, but this is usually disregarded, because all BNC outer connectors will carry the voltage the probes ground is connected to. If it´s mains voltage that can end deadly just by touching it. Should the scope not have the proper isolation against the voltages in the system it might be damaged as well.
So you should really know what you are doing and use the proper tools for the job - either by using an isolated bench power supply that allows the point connected to ground and not connecting other scope inputs to a different point/having all other connections either open or use a differential probe.