Why is a Current Transformer always connected to ground?
Why does this not affect the current flowing through the ammeter?


If you put a voltmeter across a 9 volt battery, the voltmeter would read 9 volts. Now, if you connected either side of the battery to ground (or even a hundred volts) the voltmeter will still read 9 volts.

It's no different with a current transformer - it has induced in the secondary a voltage and that voltage can drive a current into an ammeter and it forms a complete circuit and the ammeter reads so-many amps. If you made a spurious single ground connection, no current will flow into ground because there is no complete circuit to push current into or around and the ammeter will continue to read so-many amps.