In Australia and the UK at least, you are required to assess what dangers may exist in the work place and also provide solutions to make the task more safe. They are generally called Risk Assessments and Job Safety Analysis.
A Risk Assessment is generally considered more global - ie the general risks in the venue like objects suspended over head, objects flying, sharp edges etc.
A JSA is task oriented - ie you are flying a performer in Peter Pan, how are you going to do that safely, what risks exist etc.
The key point with RA's and JSA's is they should be site and time specific. So you don't just have a "single point verticle rigging, person flying" JSA that covers you for all jobs, but instead you have a "Peter Pan at the Royal Albert Hall, between the dates of 12/12/09 - 31/12/09" JSA.
All of this then ties in to SWP's - Safe Work Practice documents... which you can refer to in your JSA's and RA's and are a global document - things like correct use of ladders - maintain three points of contact, fibre-glass supports if dealing with power etc...
Usually the realm of the Technical Director... but not always. The major problem with the entire thing is that even for someone who is experienced, a full RA of a job can take 10+ hours of work, and then there are the JSA's on top of it, so generally what happens is companies will make a boiler plate RA and tailor it to the job . Mine is a 26 page document with a bunch of yes/no combo boxes which I then attach a number of floor plans and weight loading charts to submit to the OH&S committee at the venue I work. It takes about an hour per RA, and basically it gets filed in a filing cabinet and never seen again.
If there is an injury, that RA combined with our SWP folders will be our primary defence - we need to prove that all crew had easy access to the SWP's and for jobs that have RA's (anything not using just installed infrastructure and a few leads and AV equipment on a desk basically) crew know where to find the RA's and are encouraged to read them. If the RA is not deemed sufficient, then a full OH&S audit is done... After one of those, generally you are walking a little funny and have a list of "concerns" to be rectified immediately... if they let you stay open. That is why boiler plate RA's and internal SWP's are often considered company secrets - as it is known for companies to spend 100's of thousands on developing them.