Grass seems to be another example of the famed cockney rhyming slang - as a shortening of grass-in-the-park, which rhymes with "nark".
A nark is British slang for an informer - a shortening of copper's nark. This is possibly from the Romany nak for nose.

My English great grandma loved the term "nosey parker" for a busybody, and I would guess that it is linked to the Romany word too.