We have popcorn ceilings in our house and it has been brought to our attention that because our house is old, it's likely that it contains asbestos. I've looked online and can't find exactly what I'm looking for. I contacted my landlord and he told me there is no need to have my house tested because it takes years to affect your health. I have two children under the age of three and do not want to bet their health on the word of some know it all yuppie. I am aware that it does take years to affect your health and the asbestos must be disturbed to release the particles into the air, but my children are my whole world and if there is even a remote chance of them being harmed I am not willing to take it.
Please help me out if you have any helpful info regarding the actual question. (Opinions are not helpful, so please only respond if you really know.) Thanks.

Here's the Washington state law governing landlord-tenant rights and responsibilities: http://apps.leg.wa.gov/RCW/default.aspx?cite=59.18