Miller has pointed to the fact that he retains joint custody of his daughter with Moreno in seeking to refute claims of abuse. He has sued his ex-wife for defamation.
On Tuesday, he also offered to file his own paperwork for an ethics investigation into himself “to clear my name from these horrific attacks on myself and family”.
The House of Representatives Ethics Committee formally launched an investigation later in the day. The inquiry could take months to complete.
Miller and Moreno, whose divorce was finalised last year, have been involved in legal disputes for some time.
But the rancour has escalated ahead of this Wednesday’s state deadline to replace congressional nominees on the ballot.
In one police report, seen by CBS and other news outlets, Moreno alleged that during a custody exchange in February, Miller threw her against a wall, resulting “in an obvious grab mark on her upper arm and bruising to her stomach and side where she hit the wall”.
In the report, an officer also described discussions he had with a county child protection specialist a few weeks earlier about an incident where the couple’s toddler was diagnosed with a fractured clavicle.
A bruise accompanying the injury “appears to be a hand print and appears to have been inflicted”, the officer wrote in the report, according to CBS.
Moreno also told police that after her daughter returned from a stay with Miller, the child said to her: “Daddy kill you”, CBS reported, citing the police report.
Miller told CNN: “I wish you could talk to my beautiful baby girl. She can’t string together sentences like that.”
On Sunday, he alleged in a video on X that his ex-wife has “significant mental health challenges”.
“If I had assaulted her, would she have offered to cook me dinner six days later?” Miller said.
Moreno also alleged that Miller had used illegal drugs, something the congressman acknowledged in his interview with CNN.
The last time he used illicit substances was “several years ago”, he said, adding that he had also used testosterone replacement therapy, which is legal when prescribed by a licensed doctor.
A spokesman for Moreno, Stefan Mychajliw, wrote on X on Sunday: “There is a documented trove of evidence that Miller has a history of violent and dangerous behaviour and no amount of victim shaming will change that.”
His ex-father-in-law, Senator Bernie Moreno, wrote on X on Sunday that his former son-in-law should not serve in Congress.
“I believe Max Miller needs to seek professional help to end the clear pattern of abuse he has left in his wake,” posted Senator Moreno.
Many senior Republicans have so far sidestepped questions on the situation or have emphasised that these are just allegations.
Miller acknowldged to CNN that Trump had told him over the phone on Monday: “I don’t know if you’re going to be able to pull this one out.”
But he said he had told the president he would win the election, just as he said Trump had done when embattled by various accusations.
Miller is also facing a newly filed restraining order filed this week by a lawyer representing Stephanie Grisham, who was White House press secretary during Trump’s first term.
Grisham and Miller had a relationship from 2019-20.
The pair later settled a defamation lawsuit after Grisham accused an unnamed former boyfriend of abuse in a 2021 op-ed in the Washington Post.
Miller denied he was the partner in the accusation and filed a defamation lawsuit against Grisham the following year.
Grisham has separately sued Miller accusing him of breaching the terms of the settlement, which included ceasing disparaging remarks about each other.
The BBC has contacted Miller’s office and Moreno’s attorney for comment.
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