Gardai opened an investigation after videos of the incident at around 7.30 pm on September 19 went viral on social media.
The boys, two aged 14 and a 15-year-old, who cannot be identified because they are minors, are accused of various motor theft-related offences, dangerous driving, and criminal damage.
Gardai opened an investigation after videos of the incident at around 7.30 pm on September 19 went viral on social media. Footage showed a collision between the patrol vehicle and another car cheered by on-lookers.
On Monday morning, the trio were arrested by gardai from Ballyfermot, Clondalkin and Rathcoole Garda stations.
They were charged that evening and held overnight pending their separate appearances before Judge Paul Kelly at the Dublin Children's Court on Tuesday.
Garda Carina O'Hara, Garda Daniel Matthewson and Detective Garda Michael McNulty told the court the defendants "made no reply" when charged.
The 15-year-old boy is accused of unlawful use of a stolen car at Cedarbrook Avenue and using or being a passenger in another stolen car on the same date. He is also charged with dangerous driving at Cherry Orchard Avenue and criminal damage to a Garda car.
One 14-year-old is accused of being a passenger in the two alleged stolen vehicles at Cedarbrook Avenue. At the same time, the other boy is charged with unlawfully travelling as a passenger in one of the two cars.
They have not yet indicated how they will plead.
District Court president Judge Kelly noted their parents were present for the proceedings, and he granted legal aid. He noted there was no Garda objection to bail with conditions but held that only one of them must obey a curfew.
They must attend school or bail supervision programmes and remain contactable by mobile phone, and two must stay out of Ballyfermot. The judge noted they had "no business" to be in the area.
Solicitor Lorraine Stephens, for one of the 14-year-old boys, said her client's mother claimed her son was told he would not be included in the Garda youth diversion programme instead of court prosecution because he did not admit involvement. However, Garda O'Hara rejected the claim.
The court heard he had never been arrested before and had no prior convictions.
Doireann McDonagh BL, for the 15-year-old, submitted that it was unfair for her client to be ordered to obey a curfew, but he agreed to the other terms. Solicitor Peter Connolly said his client would stick to a curfew.
They spoke only to confirm they understood the terms and the consequences of breaking them.
Judge Kelly warned them they must be of good behaviour and not be in control of any motor vehicles, and breaking bail terms risked being held in custody for the duration of the proceedings.
He ordered them to appear again on November 15 for directions from the Director of Public Prosecutions to be obtained.
The two officers in the rammed Garda car have since signed off work and are receiving support.
Until age 18, the law classes the defendants as children with a right to anonymity.
Section 93 of the Children Act states no report shall be published or broadcast which reveals the name, address or school of any child concerned in the proceedings or include any details likely to lead to the identification of any child involved in the proceedings.
A fourth boy has been referred to the juvenile youth diversion programme.
That will decide if he will be suitable for their youth crime diversion scheme as an alternative to a court prosecution with the risk of a criminal record and a custodial sentence.