Thank you for your comments, gentlemen. This isn't an exercise, it is an enquiry from a police officer about an actual incident. Since he identified the bullet as a .22LR I have assumed that it is the standard lead round-nosed type, but I will check that with him.
I do have some information about ballistics, including a couple of maximum-range tables. One of these is for a 7.5mm Swiss military rifle round (streamlined bullet, 2,600 fps), which reveals that the maximum range is 4,457 yards achieved at an elevation of 34 degrees 42 minutes, with a terminal descent angle of 71 degrees 21 minutes. The other I have is for a 20mm Madsen AP round, which is surprisingly similar: max range 4,700m achieved at an elevation of 36 degrees 40 min, with a terminal descent angle of 80 degrees 19 min. The range at which the descent angle is 40 degrees for the Madsen is 3,800m, which is just over 80% of the maximum range. By interpolation, the equivalent distance for the 7.5mm Swiss seems to be in the region of 3,800 yards, which is around 85% of maximum range.
I know that the .22LR 40 grain solid when fired at 1,255 fps has a maximum range of 1,623 yards (source: NRA Factbook) which, if the 80-85% ratio applies, would suggest that the bullet could have been fired at up to 1,300-1,380 yards. This would presumably be for a high-velocity loading fired from a rifle. For a standard-velocity from a pistol, I assume that the likely range is about 1,000 yards (that's just a guesstimate). However, I do not know how accurate these figures might be. The ballistic calculator I normally use (JBM) gives lots of valuable data but not the descent angle. I was hoping that someone might have some ballistic tables for .22LR, or alternatively, a ballistic programme which does give the descent angle. However, .30Cal seems to have produced similar results to my rough estimates, so 1,000-1,500 yards is probably as close as we can get.