Is broken glass vandalism covered under comprehensive or collision auto insurance?

comprehensive

Not so clear-cut.  I think a lot also depends on HOW the supposed
damage to the glass occurred.  If the glass was struck by a mobile
object (for instance, a rolling bike), it would come under 'COLLISION
COVERAGE' regardless of whether your car was stationary.  I am almost
certain when a shopping cart  rolls into your parked car, it is
considered collision.

I am not an insurance expert, so I suggest you give you insurance
rep./agent a call to absolutely be sure.

Research Help is right.

"Part D ? Coverage for Physical Damage to Vehicle 
        * Collision vs Comprehensive 
                * Collision Insurance is auto insurance that pays for collision 
damage to an insured automobile regardless of who is at fault. 
                * Comprehensive Insurance protects against loss to an insured 
automobile caused by ANY peril not just an accident. This means that 
it includes theft, vandalism, etc. "
http://listproc.ucdavis.edu/class/200601/are142-w06/0008.html

triumfdoogooder, It is actually completely clear cut. This would
definitely fall under comprehensive. If the asker wants to confirm,
call your insurance company.

I am an Insurance Agent for a big company (which will just remain
anonymous).  There are basically 3 levels of coverage you have on a
car...Liability, Collision, and Comprehensive.  Liability coverage is
coverage for you in case you get sued in any situation to do with you
as a driver of an automobile (whether to do with injury or damage to
another party if you are found at fault).  Collision coverage, in
understandable terms, is simply physical coverage for your own car
when you are responsible for that collision (hit a tree, a deer,
another car, etc).  Comprehensive coverage is coverage for everything
else not realted to you as a driver during that situation (fire,
theft, vandalism, hail, etc).  It is very clear cut and very well
defined, you should always ask your broker or agent if you ever are
not clear on something.
But to answer your question, your situation is a little different if
it's a rental...since you do not own the vehicle then the above is not
entirely applicable.  You can either purchase additional coverage on
your own veh (which is called "Legal Liability for Damage to Non-Owned
Automobiles") which costs very little...usually less than $50/year, or
some people have coverage on their credit card for the same thing like
you do.  Other wise the rental company will send you a big fat bill
that you must pay in case of a loss.
So....moral of the story:  If you sign to decline coverage on the
rental agreement, make sure you have coverage from somewhere else cuz
basically you will be driving a car with no physical damage coverage
and if you have a claim you will have to pay back every cent to the
rental company.
...unless you "buff it out" and don't get caught!  lol
GOOD LUCK