Three deaths in South Yorkshire were referred to the Independent Police Complaints Commission last year.
A new IPCC report shows there was one death in or following custody and two apparent suicides within 48 hours of release.
Nationally there were 11 deaths in or following police custody - down from 15 the previous year, but the number of suicides was at its highest for 10 years, at 68, last year.
A South Yorkshire Police spokeswoman said: “Of the three cases, the IPCC and local investigations found no evidence of officer wrongdoing or misconduct in any of the incidents. The actions of South Yorkshire Police have not been a contributing factor to the deaths.
“Naturally, we regret the death of any person who has been in police custody. Our policy is that any person who comes into police custody is correctly treated in line with the appropriate guidance and approved practice.
“This includes a pre-release risk assessment, which determines whether that person is thought to be a risk to themselves or others.
“In the unfortunate event of a death occurring, we always evaluate the IPCC report to establish if there are any lessons to be learnt.”