Mrs May made the remark during a speech in which she repeated her belief that the Human Rights Act, which incorporates the European Convention on Human Rights into UK law, "needs to go".
Her comment.
"We all know the stories about the Human Rights Act... about the illegal immigrant who cannot be deported because, and I am not making this up, he had a pet cat."
But a spokesman for the Judicial Office at the Royal Courts of Justice, which issues statements on behalf of senior judges, said the pet had "had nothing to do with" the judgement allowing the man to stay.
The case at the centre of the row occurred in 2008 and involved a Bolivian student who said he could show he had a proper permanent relationship with his partner and should not be deported.
The Bolivian man eventually won his case on appeal because the Home Office had ignored its own immigration rules on unmarried couples.
She urgently needs to get her facts straight."
Amnesty International said Mrs May's comments only fuelled "myths and misconceptions" about the Human Rights Act.
Justice Secretary Ken Clarke, told the BBC: "The cat surprised me. I cannot believe anyone was refused deportation just because they owned a cat."
And he said repealing the UK Human Rights Act would mean "all the cases go back to Strasbourg", adding: "I think it is a good idea that we remain adhering to the Convention on Human Rights and the cases are heard here by British judges."
Its all about facts.. This guy was an immigrant, there is no evidence of any wrong doing.
Mrs May comment only serves to link immigrants with criminals, again.
In my opinion dangerous, she has a loose mouth.
She is in fact a very good reason to keep the human rights act.
You need to take an objective view, step back, and think, at this time we have tory government, end of term who knows ? in 10years it could be National Front.
The human rights act was put in place to try and prevent future atrocities, such as genocide, torture, forced labour, slave labour,
It may not be perfect or ideal, but then again nor is the world.