It comes as new measures are to be set out by Home Secretary Amber Rudd to tackle violence in England and Wales.
Ms Rudd said it is a "mistake" and "disservice" to communities and families to blame police numbers.
Today programme serious violence was a "complex crime" and "not all about police numbers", adding that she had not seen the leaked report.
"I think that you do a disservice to the communities and the families by making this a political tit-for-tat about police numbers," she said.
It comes amid concerns following the deaths of more than 50 people in violent attacks in London since the start of the year.
Labour's shadow police minister, Louise Haigh, said Ms Rudd had "serious questions to answer" after appearing to contradict the Home Office research.
She told Today that falling police numbers had "created the conditions for violent crime to thrive".
The document from February notes that forces have faced greater demand since 2012 due to an increase in recorded sex offences while during the same time officer numbers have fallen.
It says: "So resources dedicated to serious violence have come under pressure and charge rates have dropped. This may have encouraged offenders."
The analysis does go on to say that forces with the biggest falls in officer numbers are not seeing the biggest rises in serious violence.
It concludes that while pressure on resources is not the "main driver" that "triggered the shift in serious violence", it has "likely contributed".
Writing in the Sunday Telegraph at the weekend, Ms Rudd said evidence did not back up claims that reduced resources - including a fall in police officers - were the cause of more crime.
Across England and Wales, the number of police officers fell by 14%, to 121,929, between September 2010 and September 2017, according to the Home Office.
It said that out of 43 territorial police forces in England and Wales, 25 recorded falls in police numbers in the year to 30 September.
Some of the biggest falls were recorded in the West Midlands (-4.1%), Thames Valley (-2.9%) and the Metropolitan Police (-2.9%).
The Met, which has more than 30,000 officers, saw officer numbers fall by 922 over the year.
She said the strategy would focus on early intervention, tackling the drugs market - which she said was a key driver of violence - and tougher law enforcement.
Shadow home secretary Diane Abbott has called it a "small-scale" investment, claiming the government has "only just woken up" to the problem. Leader Jeremy Corbyn is to attack the Conservatives over police cuts and rising crime when he launches the party's local election campaign later.
However, Ms Rudd will commit to doing "whatever it takes" to make the streets safe as she launches the strategy - emphasising the government's determination to halt a rise in stabbings, shootings and acid attacks.
She will say: "We will take the comprehensive approach necessary to make sure that our sons and daughters are protected and our streets are safe.
"As a government, we will never stand by while acid is thrown or knives wielded."
The strategy, which was first outlined last year, will target the so-called county lines drug distribution model where city gangs courier heroin and crack cocaine to rural or coastal towns, and will call on social media companies to do more to remove violent gang content.
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