I personally wouldn't chose a crossbow, but I can see where they could come in handy in some situations.

A shotgun tells the rest of the zombie horde where you're standing.
Lara Amber

True, but arrows and crossbow bolts kill by hemorrhage and that takes time.

Yes, yes I know in the movies the guy hit by an arrow/crossbow bolt always gasps, grasps the arrow and collapses silently. But in the real world on the hunting shows I watch on the Sportsman and Outdoor channels deer and wild pigs almost never collapse silently on the spot. The pigs squeal and 99 times out of 100 (and I've watched hundreds of shows) they run off, usually dozens if not hundreds of yards.

If you're worried about making noise when forced to shoot a looter use a small caliber gun and wait until they're inside your home.

Morally and legally you just about have to do that anyway 'cause you can't just shoot anyone wandering across your front yard.

So if you want to use a crossbow, be sure you're wearing a pistol 'cause you'll likely have to shoot'em (or their friends) again.