A martial arts instructor accused of violently killing a family in western Sydney has not applied for bail at his first court mention on three murder charges.

Kwang Kyung Yoo, 49, was charged with the murders on Wednesday night as he remained under police guard at Westmead Hospital.

He is accused of murdering a 41-year-old woman and her seven-year-old son at his taekwondo school in North Parramatta on Monday night.

He then took the woman’s white BMW to Baulkham Hills, police say, where he allegedly fatally stabbed the 39-year-old father of the child.

He presented himself to the hospital with stab and slash wounds, claiming the injuries were from a supermarket car park incident, investigators allege.

Police attended the hospital, placing Yoo under arrest late on Tuesday and charging him with the murders less than 24 hours later.

His lawyers briefly appeared at Parramatta Local Court on Thursday, when they did not apply for bail.

The 49-year-old did not appear by video link from his hospital bed.

Police prosecutors will have to supply Yoo and his lawyers with a brief of evidence by April 16 and the matter will be back in court two days later.

He has yet to make any pleas.

– AAP