The 39-year-old man, who lives in Knowsley, was questioned in connection with an allegation of rape, common assault and criminal damage on Tuesday.
Police said the officer, who was off-duty at the time of the alleged incident, had been placed on restricted duties and bailed until 6 December.
The incident has also been referred to the Independent Police Complaints Commission (IPCC).
Merseyside Police said the officer was arrested on 10 October.
A spokesman said: "The arrest was made following allegations about off-duty incidents."
The accused officer will have no contact with the public as part of his restricted duties, he added.
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