I'm not sure that 'Liar, Liar, pants on fire'
is a nursery rhyme: it's more of a playground taunt and complete in itself. I wonder whether you are thinking of the Hillaire Belloc poem '
Matilda', in which a little girl of that name often cries 'Fire!' when there is no such fire. Eventually, of course, one day a fire
does occur and she gets burned to death, since nobody believed her when she called for help. You'll find the poem if you click
http://www.btinternet.com/~p.wilkinson2000/Matilda
Belloc.htm