The fatal shootings of a Hofstra student and the paroled robber who held her hostage has shaken Long Island, raising troubling questions about police and parole procedures that need to be resolved.

As mourners gathered at services for Andrea Rebello in Tarrytown this week, family members continued to question whether police should have used deadly force before negotiating with the armed robber.

Meanwhile, Nassau Executive Ed Mangano appropriately called on Police Commissioner Thomas Dale to investigate the circumstances leading an officer identified as Nikolas Budimlic, to fatally shoot Andrea Rebello and Dalton Smith.

Police say Rebello was killed while being held at gunpoint by Smith, who had invaded the Uniondale home Rebello shared with other students.

A felon with a long and increasingly violent rap sheet, Smith was back on the streets despite violating parole twice in two years. Why was he set free? And what did the responding officers know about the hostage situation? Did they follow police procedures?

Mangano has rightly pledged to make Dale’s report public, and Nassau DA Kathleen Rice should also make public her investigation into the facts in this case. She has done so in other shootings involving law enforcement officers.

Let’s get all the facts.