The Metropolitan Police has asked the Home Office to pay £38m for its Grenfell Tower fire investigation.
The London force has submitted an £11.1m claim to cover overtime and extra costs in 2017-18.
It will also request £27m to fund the entire costs of the investigation, which involves 200 officers and staff, for the 12 months from April 2018.
Finance director Lynda McMullan said: "We don't think it's reasonable for us to pick up all the costs."
BBC home affairs correspondent Danny Shaw said the investigation into the blaze was one of the biggest and most complex inquiries in the force's history.
Seventy-one people were killed in the west London tower block fire in June.
Last month, a public inquiry into the Grenfell Tower fire, headed by Sir Martin Moore-Bick, heard that the Met was investigating offences including manslaughter, corporate manslaughter, misconduct in public office and breaches of fire safety regulations in relation to the fire.
The force has gathered 31 million documents and 2,500 physical exhibits. Some 1,144 witnesses have given statements and 383 companies are part of the investigation.
The inquiry plans to deliver an interim report into the fire's causes and the emergency response by next autumn.
The Met has also requested extra government funding of £7.8m to help pay for policing following last year's terror attacks.
At a meeting of the London Assembly, Sophie Linden, deputy mayor for policing and crime, said police officer numbers in London were set to fall "significantly below" 30,000 despite the funding settlement announced by ministers before Christmas and an increase in the policing precept.
There are currently 30,300 officers in the Met.
In November, Prime Minister Theresa May said the government would fully fund the costs of dealing with the Manchester Arena attack.
Her promise came after the initial government offer of £12m was criticised by Greater Manchester mayor Andy Burnham, who estimated that the cost would be £28m.