A woman has been charged with murder after police found the body of a preschooler at a home on the New South Wales Central Coast.

Police rushed to the home at Wyong after a 32-year-old woman presented to the local police station on Saturday.

Officers tried to speak to the woman but they were unable to do so.

The body of the child, believed to be a four-year-old boy, was found inside the home late in the afternoon with significant arm injuries.

Tuggerah Lakes police district commander, Supt Chad Gillies, told reporters on Sunday morning that police believed the 32-year-old lived alone with the child, with whom she had a “domestic relationship”.

Gillies said the woman – who was known to police – drove to a station, which triggered a search of her apartment, where the child was found dead. Officers declared a crime scene, arrested the woman and seized her car along with other evidence.

The superintendent said police and paramedics faced what was an “extremely confronting scene” for even the most experienced of officers.

“Whenever a child is a victim of violent crime, and whenever a child is [allegedly] murdered, it strikes at the core of community,” he said. “That is why it is absolutely important we work through this methodically.

“We try to understand what’s happened [and] why it’s happened.”

The woman was charged on Sunday with murder (domestic violence). The woman’s lawyer Neusha Ghahreman did not apply for bail on behalf of her client during a brief hearing on Sunday.

The case was adjourned until 1 September.

Police were still at the scene on Sunday morning and will investigate what happened to the boy with help from the homicide squad.

“We still have to formally identify that child, and we are working with family as we speak,” Gillies said.

“We are still in the infancy stages of this investigation.”