There's a website called Phrase Finder that gives this explanation to the expression, rat-arsed:
"This addition to the myriad terms for being drunk entered the language in Britain in the 1990s. It is sometimes shortened just to 'ratted'. It is a follow-on to the earlier phrase 'as p*ss*d as a rat'. There wasn't any particular reason to pick on rats, the choice seems almost arbitrary. Other creatures which have been used in similar phrases are newts, ticks, skunks - even lords:
As drunk as a lord. As drunk as a skunk. As p*ss*d as a newt.
As tight as a tick.
Parsley3 Mon 21-Dec-20 11:04:13
Love it. Mouse bottomed sounds so much more genteel. One doesn’t want to be common.
My late mother-in-law hated any crudeness in spoken language. She had to laugh though when her oldest daughter had embarrassing flatulence caused by baby movement in late pregnancy and I referred to it as: Botty Burps.