Paul Wallace, 47, of Willowdale, Hull, pleaded guilty to the charge at Hull Crown Court on Wednesday.
He will be sentenced at a later date.
Jonathan Sandiford, prosecuting, said the prosecution's case was that Wallace, a police constable with Humberside Police, took £65 from the wallet but the defendant claims to have no memory of whether he took the money.
He said Wallace then tried to cover up the theft by committing a number of acts that perverted the course of justice, including adding notes to his police notebook.
Wallace admitted fabricating an exhibit, amending his police pocket notebook by adding notes making reference to the fabricated exhibit, placing the fabricated exhibit in the property store at Clough Road police station, and causing another police officer to search for and recover the fabricated exhibit from the property store.
He was originally also charged with a count of theft, which he denied, but will not face trial on that charge due to the seriousness of the perverting the course of justice offence.
Mr Sandiford said: "Count Two (perverting the course of justice) represents the gravamen of offending for a serving police officer."It is not necessary to have a further trial on Count One (theft)."
Sentencing was adjourned until Monday June 24.
Judge John Thackray QC told Wallace that he could face jail.
He said: "Paul Wallace, you have pleaded guilty to a very serious matter and you will be sentenced on Monday next week.
"I will grant you bail till Monday next week but that is no indication of sentence. All options are open, including immediate imprisonment."