A man has been arrested for allegedly assaulting a woman who was found unconscious and later treated at Royal Darwin Hospital for a significant head injury, NT Police said.

NT government crime marketing manager Sita Bacher said in a statement that about 1pm Thursday police received reports a 34-year-old woman had been assaulted and was unconscious at a home in Fawcett Court, Malak.

She said the woman was taken to Royal Darwin Hospital with a significant head injury.

Police referred to it as a domestic violence assault, and said a 38 -year-old man, who knew the woman, was arrested nearby and remained in police custody.

The agency is also calling for information about another domestic violence related assault in Malak on January 19, that police did not make public at the time.

Ms Bacher said that about 11pm a 36-year-old man was assaulted in the vicinity of Rickards Court, Malak, suffering leg injuries requiring treatment at Royal Darwin Hospital.

She said police believed the man was assaulted by a someone who knew him, and were looking for the person. Despite asking the public for information police did not give a description, including the sex, of the wanted person.

Anyone who witnessed either assault is asked to call police on 131 444, or make an anonymous report through the Crime Stoppers website or call 1800 333 000.

If you or someone you know is experiencing difficulties as a result of domestic violence, support services are available including, but not limited to 1800RESPECT (1800737732) or Lifeline 131 114.