As designed and used, a current transformer tries to maintain its secondary _current_ as a strict proportion of its primary current. It tries to hold this output current no matter what the secondary voltage. There is no danger to shorting the secondary; in this case the target current will flow, without much voltage needed to 'push' it through the shorting bar and secondary resistance.
If you open the secondary circuit, the secondary voltage will get extremely high, in an attempt to maintain the secondary current in proportion to the primary current. In some circumstance the voltage can get high enough to damage insulation or arc between terminals. So for a 'Current Transformer' the safe state is with the secondary shorted.
In basic physics, a CT is just like any other transformer. You have a primary coil, a magnetic core, and a secondary coil. The current flow in both the primary and secondary coils creates a magnetic field, which then induces voltage in _both_ of the coils. The relationship between the induced voltage and the applied voltage determines what the transformer is doing.
In a conventional distribution transformer, or in a PT, the primary and core are designed so that the voltage induced in the primary coil is nearly the same as the applied primary voltage. This induced voltage is what limits the primary current to a reasonable value. Voltage is also induced in the secondary coil. If current is allowed to flow in the secondary coil, it tends to reduce the magnetic field strength, which reduces the voltage induced in the primary, so more primary current flows.
In a CT, the primary and core _do not_ limit current much at all. The primary 'coil' is just a short straight length of wire going through the 'donut' of the core, and the core is just the small donut. The 'primary voltage' of a CT is ideally a few millivolts. In use, this primary voltage is placed in series with the load being metered, and it is the load which determines the current flow through the primary.
You still have primary current flowing, which creates a magnetic field, which induces voltage in both primary and secondary coils. Just as in the transformers mentioned above, secondary current flow will reduce magnetic field strength and thus the voltage induced in the primary. But unlike a distribution transformer, this reduced primary voltage does not cause more primary current to flow. Again: the primary voltage is perhaps a few millivolts, and the primary current is limited by the load being measured.
As mentioned above, the primary is a single 'turn'. The secondary is perhaps 200-2000 turns. So the voltage induced in the secondary is 200-2000x the voltage across the primary. If the secondary is opened, then you get no balancing current reducing the magnetic field strength. The core saturates and the primary voltage rises to the maximum that the small core and single turn can sustain. Because of the small core and low turn count, the primary voltage is still quite low, and the primary current will remain limited by the load. But even if the primary voltage makes it up to a couple of volts, the turns ratio multiplier can make for a very high secondary voltage.
So whatever you do, make sure you have a proper 'burden' on the secondary side of your CTs.
-Jon
(Apparently I was writing while Gar was posting. )