Babbitt was the only person to be killed on January 6 when thousands of Trump supporters stormed Congress.
Her family say that video of her being shot proves that the plain clothed officer who did it did not issue a verbal command, and that the US Capitol Police is liable for her death.
They told The Washington Examiner they will sue for wrongful death and are seeking $10million in damages.
'It's not debatable. There was no warning. I would call what he did an ambush. I don't think he's a good officer. I think he's reckless,' her family's attorney Terry Roberts said.
Roberts also said that the fact no one appears to be ducking for cover in the moments before Babbitt was shot also suggests that the cop gave no verbal warning.
'If he's yelling, they certainly aren't showing any reaction to it. If he was giving any kind of warning, why didn't they react?' he said.
An attorney for the Capitol cop who shot her, who has not been named, said that he did issue verbal commands but that they weren't audible on the video because he was wearing a mask.
'It's a false narrative that he issued no verbal commands or warnings.
'He was screaming, 'Stay back! Stay back! Don't come in here!' the officer's lawyer, Mark Schamel, told Real Clear Politics.
He added that he was within his rights to shoot.
'He was acting within his training. Lethal force is appropriate if the situation puts you or others in fear of imminent bodily harm.
'There should be a training video on how he handled that situation. What he did was unbelievable heroism,' he said.
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