Lawyers for Homes for Haringey - whichmanages council housing in Haringey, north London - say Barbara Fari lied abouthow badly she was hurt and should be found to be in contempt.
Mrs Fari, of Tottenham, northLondon, has disputed "exaggeration" allegations.
Mr Justice Spencer is scheduled to make a decision following a High Court hearing in London.He has said that, if found to be in contempt, Mrs Fari could be jailed, given a suspended prison sentence or fined.
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The Tooting MP has been the frontrunner in the counting process ahead of Tory challenger Zac Goldsmith.
It's not just London where elections have been taking place today. There were council elections taking place across the home counties.
A list of results for London Mayor and the London Assembly