A judge has tossed an official misconduct charge against a Hempstead police officer who’s accused of groping a woman outside a restaurant last year while off-duty.

Officer Louis Arcila, 49, pleaded not guilty after his October arrest and still faces misdemeanor charges of sex abuse and endangering a child’s welfare.

Prosecutors have alleged Arcila, while out of uniform but with his police badge on his hip, followed a woman from a Hempstead restaurant on June 28 before getting in her car and inappropriately touching her in front of her children, ages 3 and 10.

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Prosecutors said the veteran officer mentioned in earlier conversation inside El Rancho Catracho that he was a cop, and argued he “used his apparent authority as a police officer” to gain access to the woman in order to grope her.

However, acting State Supreme Court Justice Terence Murphy found while grand jury evidence showed Arcila made “degrading and inappropriate” boasts to the woman Arcila was sexually attracted to, there wasn’t official misconduct.

“While he did carry his badge on his belt, there was no evidence offered that he presented his badge in any official capacity to the complainant in order to engage her in conversation,” his April 6 decision said.

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Arcila’s Garden City attorney, William Petrillo, on Friday called the charge dismissal “the first step toward the complete exoneration of this police officer.”

However, Nassau District Attorney Madeline Singas’ office filed notice this week that they’re appealing to a higher court for a reversal.

“The allegations of misconduct facing this defendant are very serious. We disagree with the judge’s decision,” said Singas spokesman Brendan Brosh.

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Petrillo said any claim a badge was displayed is false and “added later” to boost the woman’s civil legal case. The defense also maintains the woman told police Arcila didn’t actually touch her.

Records show a Hempstead lieutenant wrote a memo saying the woman told police on June 28 an off-duty officer “reached out his hand to her and tried to touch her chest” and “she pushed his hand away” before he made contact.

She told a Nassau police internal affairs official on June 30 an off-duty officer, who looked drunk and got into her car uninvited, “attempted to grab her breasts repeatedly,” but she pushed him away, records also show.

However, Singas told reporters after Arcila’s arraignment that the alleged victim “has been consistent in her statements to us and consistent with what she told 911.”

The woman’s civil attorney, Xavier Palacios of Mineola, said Friday he filed legal notice last year that his client planned to sue Hempstead Village, its police force and Nassau County.

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The 30-year-old Hempstead woman took action because “she doesn’t want her daughter to feel that this is how authority acts toward women,” he said.