I'm back from a long weekend in Lake Tahoe for a birthday party which led directly into two nights on a commercial. (Hi Dino, it was nice to meet you. Welcome).
Someone had asked a while back that I do a post on having cameras directly overhead. This is a great idea for a post especially since I saw it asked just a couple of days ago on some other production related site.
Always safety the camera when it is on a crane. Now, usually the head techs, if you have a Libra or some other such head that comes with a tech, will safety it themselves with a hard mount safety. This is fine and you're covered in this instance. However, always make sure the matte box and any shade or eyebrow type device is safetied. These things are usually the first to go, so just run some bailing wire through them and make sure they stay put. You don't usually have to physically safety the head to the crane. A castle nut with a few taps from a hammer or a wrench on it isn't going anywhere, but always keep your eyes open. In the instances where the head tech doesn't have a safety, or you don't have a head tech, get yourself a daisy chain (long piece of webbing sewn into a line of loops so you can make it any length) and a couple of caribeaners and run a safety from the camera to the head. Each camera is different but they sall generally use support rods for the lenses, have a handle on top, and a few have some 3/8 threaded holes in them for rigging possibilities. If there's a threaded hole in a handle etc. you can screw in a screw eye and safety through that. Generally, Arris and Moviecams tend to have lots of neat little holes to screw in something in to tie off to. If there's not any (Panavision sometimes doesn't give you much to work with), you have to get creative. Usually, I put a choke on the rods as close to the camera body as I can get and run from there to the handle and put a second choke on it and from there to the crane (or head). You have to be careful how you run it to make sure it doesn't interfere with the movement of the head.
When you're not on a crane, sometimes you have to safety a camera that is on a dolly looking straight down over an actor. I usually will safety these too. (I say usually because you have to look at each situation and see what the dangers are) You can drop a line from the perms or grid if you're on stage, or even set up a "goalpost" over the camera with a couple combos and some speedrail and go from that. Like I said, you have to assess the risks for each shot and decide what the dangers are. You don't have to safety the the thing every time it's four feet off the ground, but if it's six or seven, and shooting straight down on an O'Connor, you might need to.