That depends on the Voltage of the bulbs in the turn signals and if a Voltage converter is used to supply power to the turn signals.
If a Voltage converter is being used then the turn signal's bulb Voltage should be 12 Volts and Voltage converter would be wired to the scooter's battery pack and the turn signals wired to the Voltage converter.
If a Voltage converter is not being used then the turn signal bulbs would need to be rated at the same Voltage as the battery pack in the scooter, then the turn signal circuit could be wired directly to the scooter's battery pack.
A separate battery could be used to power the turn signals however this would be a complicated way to wire them and the separate battery would require its own battery charger to recharge it. All turn signal installations that I have seen use the scooter's battery pack as their source of power.
Please let us know if you have any questions.