The father of a man who died in the care of Southern Health NHS Foundation Trust has made a criminal complaint.
Richard West, from Southampton, Hampshire, has accused the Trust of "producing false and misleading information" under the 2014 Care Act.
His 28-year-old son, David West, had a history of mental health problems and died from a drugs overdose in 2013 following care provided by Southern Health.
The former police officer told BBC News: "We're talking about the deaths of people, this is really serious stuff.
"Behind all the figures there are lots of families that are in turmoil and, if you aren't getting the correct information, they're not providing the right information, how can people really judge them and assess them?"
A Hampshire Police spokeswoman said: "Hampshire Constabulary can confirm it has received a complaint against Southern Health NHS Foundation Trust relating to an allegation of providing false or misleading information contrary to Section 92 of the Care Act 2014.
"This complaint will now be assessed and investigated. It would be inappropriate to comment further at this early stage of our inquiries."
A spokeswoman for Southern Health said: "We understand that Hampshire Police have received a complaint about Southern Health. We will co-operate fully in any police inquiries related to this matter.
"At this stage, the police have not formally notified the Trust of any investigation, so it would not be appropriate to comment further."
Last month, Health Secretary Jeremy Hunt ordered a review into how deaths are investigated by NHS trusts following a report into Southern Health which showed the Trust had failed to probe the deaths of hundreds of people since 2011.
Southern Health is a mental health trust providing services to 45,000 people across Hampshire, Dorset, Wiltshire, Oxfordshire and Buckinghamshire.
The NHS England investigation was carried out by audit firm Mazars and looked at patients who had received some care from Southern Health in the 12 months prior to their death in the period between April 2011 and March 2015.
The report showed that of the 10,306 deaths in the period, 722 were categorised as unexpected and only 195 were treated by the trust as serious incident requiring investigation (Siri).