On Tuesday, jurors were read an email sent by Dr Evans to the National Crime Agency (NCA) in May 2017, ahead of his involvement with Cheshire Police.
In his message to "Nick" at the NCA's national injuries database, Dr Evans wrote: "Incidentally I've read about the high rate of babies in Chester and that the police are investigating.
"Do they have a paediatric/neonatal contact? I was involved in neonatal medicine for 30 years including leading the intensive care set-up in Swansea. I've also prepared numerous neonatal cases where clinical negligence was alleged.
"If the Chester police had no-one in mind I'd be interested to help. Sounds like my kind of case.
Ben Myers KC, defending, said to Dr Evans: "This is you putting yourself forward. In effect, touting for this job."
"My opinions are impartial and independent.
"I also give evidence to law firms representing defendants. In the last five years I have given more reports relating to defendants than the police or the prosecution."
Dr Evans replied: "I was offering my professional opinion if that was in their interest."
A medic has denied "touting" for the job of assisting a police probe into baby deaths and "giving them what they wanted", the murder trial of Lucy Letby heard.
www.shropshirestar.com