What sort of insulation is it ? Loose fill or blanket ? Back in the 1980's there were a few scares about the loose fill type containing some asbestos but those were really confined to Canada and Northern USA, so it's highly unlikely that your insulation is dangerous.
You could ask your local authority (probably Environmental Health Department) to check out some samples of the insulation (I'm not sure how much it would cost, if anything) but don't go getting samples yourself, it's a specialist job.