Artex contained asbestos up until 1980. It requires chemical analysis to find out if your artex contains asbestos and if you are in any double, please assume it does. If you are asking this question because you want to remove some, please see the project on the website called Artex Removal. It can be done safely this way but do not attempt to sand it or scrape it off dry.
X-Tex Textured Coatings Remover is probably the safest way to remove artex contining asbestos fibres. Do not waste your time getting it tested as it will cost a small fortune for someone to come and do the test. I always feel that you should just assume that if it is pre 1985 that it will contain asbestos.
This product will encapsulate the artex and keep it wet at all times and prevent any dust which is the problem. You can quite safely remove artex as long as it stays wet or damp. People say that steaming will keep it wet, but it will soon dry out once it is on the floor and then will create a dust, and the heat burns like hell.
Skimming over or re-boarding used to be an option years ago but I am sure these days you would not be able to sell your home if this is detected and would have to remove all of the artex before hand. See the artex removal project in the projects section.