The first question would be - what type of CT was it? Bushing-type/LV switchgear type? Medium-voltage dry-type? HV oil-filled type?
When a CT is operated open-circuit, the core is saturated. Depending on the design and function of the CT (meaning how many secondary turns, cross-sectional area of the core, and primary current level) very high voltages can also be present on the secondary winding.
Therefore, damage can occur in 2 ways:
1 - when the core saturates, a lot of heat if produced. The heat generated is a function of the core size and primary current level. This excessive heat can damage the magnet wire insulation, the lead-wire insulation, the insulation between winding layers, etc... This could lead-time a turn-to-turn or layer-to-layer short.
2- when high voltages are present across the secondary winding, insulation can be damaged internally and/or externally. Normally, there is arcing across the secondary terminals and the damage occurs outside of the core/coil, but not always.
If the unit is a low-voltage CT, then insulation resistance (Megger) and excitation tests would be recommended.
If the unit is a dry-type MV CT, same tests, plus possibly a partial discharge test if you have access to that kind of test equipment.
If the unit is a HV oil-filled unit, add in DGA test on the oil.
If the unit was a MV or HV CT and the core had protection accuracy ratings and the unit was open-circuited in the range of 1 hour, I would be very careful about re-energizing the unit without performing off-line tests like partial discharge. And if you do continue to use the unit, understand that the useful life may have been shortened.