Lord Janner signed a House of Lords document dated 9 April, seven days before the CPS confirmed it would not prosecute due to his Alzheimer's.
The allegations relate to children's homes in Leicestershire, where he was a Labour MP, in the 1970s and 80s.
Leicestershire Police said it was looking into the letter's implications.
The force, which led the latest investigation into Greville Janner, also said a number of new alleged victims had come forward since it was announced no charges would be brought.
Peter Garsden, from the Association of Child Abuse Lawyers, said he was preparing a civil case against Lord Janner and Leicestershire County Council on behalf of one of the alleged victims.
"We have been doing very little for the last two years because we have been waiting for the police investigation to reach a conclusion ... but now we are able to pursue our civil claim."
The Cardiff-born peer, 86, has always denied any wrongdoing.
On 16 April, current Director of Public Prosecutions Alison Saunders said there was enough evidence to prosecute the peer for 22 sex offences against nine people but that this would not happen because he was now too sick to stand trial. He was diagnosed with Alzheimer's disease in 2009.
Ms Saunders also said the CPS had been "wrong" not to prosecute following investigations in 1991 and 2007.
It has now been confirmed by a House of Lords spokesman that Lord Janner signed the letter, requesting a leave of absence, which arrived a week before the decision was taken.
Leicestershire Police said the decision not to charge was "extremely worrying" and further legal action was being considered.
A peer ruled too unwell to face child abuse charges signed an official document just days before the decision was taken, it has been revealed.