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".
More on this and other North Yorkshire stories
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."

Members of the drivers union Aslef are due to walk out for three days in the dispute over driver-only trains.
Southern's parent company Govia Thameslink (GTR) has asked the Court of Appeal to overturn last week's High Court refusal to ban the strike action.
A decision will be given at the end of the hearing, due to last all day.
Lord Justice Elias, sitting with Lord Justice Lewison and Lord Justice Lloyd Jones, have been asked to overturn the refusal to grant an injunction blocking the "unprecedented" action.
GTR has already been hit by a series of strikes by the RMT union in a long-running dispute over the role of conductors.
Drivers are due to strike on Tuesday, Wednesday and Friday, with a week-long walkout planned from 9 to 14 January.
Southern said given the timing of the Court of Appeal's decision, it would be too late to get trains and drivers in the correct position for Tuesday, and any services it could run would be "extremely limited".
Angie Doll, passenger services director, said: "We hope for the sake of our passengers our application to the Court of Appeal is successful.
"Even if we are able to stop the strikes through the court, services will still be very heavily  impacted tomorrow.
"We will work through the night to try and provide as many services as possible, but we are still advising passengers not to travel as we will not be able to offer a robust service they can rely on.
"We are sorry but the industrial action by Aslef leaves us no viable alternative, but be assured we will do all we can overnight," she said.
The RMT union, which has been staging strikes since April, is also planning further stoppages either side of Christmas.
00:01: Tuesday 13 December to 23:59 Wednesday 14 December (Aslef)
00:01 Friday 16 December to 23:59: Friday 16 December (Aslef)
00:01 Monday 19 December to 23:59 Tuesday 20 December (RMT)
00:01 Saturday 31 December to 23:59 Monday 2 January (RMT)
00:01 Monday 9 January to 23:59: Saturday 14 January (Aslef)
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.
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Strike-hit rail operator Southern has warned passengers not to travel on Tuesday, irrespective of the outcome of a last-ditch bid to halt a walkout.