It's actually a glass tube that's suspended within another plastic tube that has epoxy applied to the ends to act as a shock absorber. It'd require some pretty serious abuse before it broke.
Should it break: The actual radioactive component in the vial is an isotope of hydrogen, which is much lighter than air; the tiny amount gas would immediately disperse and float away. Even if you were standing directly over a freshly broken vial, odds are the gas would be too dispersed for even a single molecule to reach your breathing space. If the vial were in your hand or pocket - again, it's a radioactive gas and not solid or fluid, it would simply float off and away, no more glow from your vial.
Worst case scenario: You break the vial on a table/desk, then IMMEDIATELY cup your hands around the vial and place your face directly over it and inhale deeply. If this were to happen, you'd receive as much radiation as ...a dental x-ray.
That's the beauty of the tritium vial design, rather than relying on the radioactive substance itself to glow, it uses a strong phosphor that glows brightly with very little energy, so you can use a remarkably weak source of radioactivity to produce a glow. The beta radiation that comes off of a tritium vial cannot penetrate tissue paper, and can only make it about a quarter inch from the vial in open air before dissipating. It's so weak that even if you were to set a Geiger Counter on its most sensitive setting, then press the probe directly onto the vial, it would not register a reading at all.
) Small quantity transport usually isn't prohibited, even in the US tritium watches are sold and shipped via regular mail.
