The figures have been released by the Independent Office for Police Conduct (IOPC).
South Yorkshire was the highest force in the county for the number of overall deaths with a total of 17.
Out of the 17 deaths, five people died in road traffic accidents, one death was in or following police custody and four were apparent suicides following custody. There were seven other deaths following police contact.
West Yorkshire Police recorded 16 deaths overall. Of the 16 deaths, five people died in road traffic accidents, one death was in or following police custody and two were apparent suicides. There were eight other deaths following police conduct.
In North Yorkshire there were four deaths, three were apparent suicides following custody and there was one other death following police conduct.
Humberside Police recorded two deaths from apparent suicides following police custody and one other death following police conduct.
Across England and Wales, a total of 42 people died in road traffic accidents involving the police in 2018/19 - the highest number in a decade and an increase of 13 on the previous 12 months.
Of the 42, 27 were men and 15 were women, with 22 of those killed aged 18 to 30, and eight over 60.
The oldest victim of a road traffic incident involving police was a 93-year-old woman pedestrian, who appeared to fall in the road in "very close proximity" to a force van on general patrol.
Elsewhere, the figures showed a total of 16 people died in or following police custody last year, down from a 10-year high of 23 in 2017/18, while three fatal police shootings happened in 2018/19, compared with four the previous year.
There were 63 apparent suicides following police custody, up six from the previous year.
Meanwhile, a total of 152 people died in other incidents involving police contact during 2018/19 - down from 175 the previous year.
In total, the watchdog investigated the deaths of 276 people, down from 288 the previous year.
"This reflects the importance of ongoing work, to which we have contributed, to ensure police custody offers as safe an environment as possible.
"However, it is of concern that, again, there is a high proportion of people dying during and immediately after custody who are vulnerable through mental health and links to drugs and alcohol."
He said the increase in pursuit-related deaths pointed to "a continued need for ongoing scrutiny of this area of policing".
He said: "Police drivers need to be able to pursue suspects and respond quickly to emergency calls as part of their duty, but it's not without risk.
"This includes risks not only for the police and the driver of any pursued vehicle, but for passengers, bystanders and other road users.
"Pursued drivers bear responsibility for their own actions but police officers should also take into account risks to the public and only undertake a pursuit where it is safe to do so, and where authorised."