The complaint, the DUP said, was made to the ombudsman by Paul Givan MLA.
It comes after Health Minister Edwin Poots told MLAs on Tuesday that the PSNI had to be investigated over its handling of the allegations.
Mr Poots said Áine Adams - who was abused by her father Liam during a six-year period over 30 years ago - was let down by police and her uncle.
The DUP minister said: "I have to say that Áine Adams was let down by the RUC, she was let down by her uncle Gerry Adams and she was let down to an extent by the PSNI.
"The PSNI has questions to answer," he added.
"It needs to answer those questions publicly, and that is why the ombudsman needs to look at the PSNI's work to date."
"The public should be in no doubt that failure to report child abuse is something there should be zero tolerance of and that's why I met the Chief Constable Matt Baggott yesterday to indicate that they haven't done their job as well as they should have," he added.
Police said that, during the meeting, Mr Baggott explained that "the authority for prosecutorial decisions, and any action necessary, correctly rests with the PPS".
The Health Minister is entitled to make a complaint to the Ombudsman should he wish to do so.
In a statement, a PSNI spokeswoman added: "In the light of the recent trial and guilty verdict the PSNI will now review the evidence and examine any further investigative opportunities.
"This follows the original submission of a file, having taken legal advice, recommending no prosecution in relation to Gerry Adams."
The file was submitted to the PPS in October 2011.
On Tuesday evening, the Police Ombudsman said: "We have received a complaint that police did not properly investigate a witness statement made to them in connection with an allegation of child sex abuse."
The current Director of Public Prosecutions, who was his solicitor at the time, has also ordered a review of the decision taken by the PPS.
Barra McGrory QC asked the Attorney General John Larkin QC to review the handling of the case due to the "considerable public interest surrounding the decision not to prosecute" the senior political figure.
There has been mounting criticism over Mr Adams' nine-year delay in informing police about a confession his brother made to him in 2000.
Speaking in Dublin earlier, Gerry Adams said he is confident he hasn't committed any offence in relation to his brother's sexual abuse case - and fully co-operated with authorities.
I know that I committed no offence and I know I did what I considered to be the right thing and I cooperated fully with the PSNI, with the PPS, with the court.
"I gave evidence in the court, so I don't have any concerns about that," he said on Tuesday.
"I'm obviously concerned that as members of my family pick up the newspapers this morning and, on the back of this press conference, will pick up the newspapers tomorrow morning, they wonder why there's such an inordinate attention on this and on me."
The Sinn Féin president singled out the DUP and Fianna Fáil, declaring he was a victim of a political agenda on both sides of the border.
During a first trial of Liam Adams earlier this year, which was abandoned for legal reasons, the former West Belfast MP testified that he confronted his brother when they met in Buncrana, Co Donegal, in 1987 and that Liam Adams had denied the abuse.
Gerry Adams said the first time his brother confessed to him was when they were out walking together in the rain in Dundalk, Co Louth, in 2000.
He told police about the confession a month before the allegations were first made public in a UTV documentary in 2009.
At the time Gerry Adams told UTV he had always believed the allegations.
Liam Adams, who was found guilty of raping and abusing his daughter Áine, will be sentenced next month.