Raining cats and dogs

[James A. Landau]

I heard the following story about the phrase "raining cats and dogs" and
would like to know if it is true, etymythology, or undecided:

"The phrase comes from the days when most roofs were thatch.  Now thatch
contains seeds, which means it attracts mice and rats who eat the seeds.  To get
the rhodents out of their rooves, people would turn their cats and dogs loose
on the roof.  When it rained, the felines and canines were washed off the roof,
hence the expression."

     - James A. Landau