Gavin Egan, 34, was found in Peasholm Park, Scarborough, on 24 February 2016.
The Independent Police Complaints Commission (IPCC) said PC Helen Hardie "had a case to answer for gross misconduct".
The force said it "disagreed with the content of their [IPCC] report".
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In its report, the IPCC said an ambulance had gone to the park after a member of the public had contacted them to say he had pulled a man out out of the lake.
A paramedic searched the park for about 38 minutes but could not find the missing man, so he called the police.
PC Hardie attended the scene at about 04:00 GMT.
The IPCC report said: "A four-minute search was carried out before PC Hardie left the area, she did not seek assistance and the incident log was closed soon after."
It added that the officer concluded the missing man had fled the scene "despite a paramedic's view that he would be incapable of such action because of freezing temperatures".
She later told an inspector "there was no evidence a man had been pulled from the lake".
Mr Egan's body was found at about 11:30 GMT.
The IPCC investigator said that in his opinion "PC Hardie had a case to answer for gross misconduct".
In a statement, North Yorkshire Police said: "We disagreed with the content of their report and their finding that it amounted to gross misconduct.
"We appealed their report and it was subsequently agreed with the IPCC that a misconduct meeting would be held.
"This has been carried out and the officer has been issued with a written warning."
A North Yorkshire Police officer made "errors" in the search for a missing man who was later found dead in the lake of a public park, the police watchdog has found.