In an apartment in an apartment building in Essen, a man is said to have seriously injured a 26-year-old on Monday morning.
She was taken to hospital with stab wounds.
After initial investigations, the police assume a relationship act, said a police spokeswoman on Tuesday.
A suspect reported to the police shortly afterwards.
Essen - He is currently being questioned.
Neighbors had alerted the police at around 9 a.m. because they heard screams.
The officers arriving found the victim and had them taken to a hospital.
According to witnesses, the search for the suspect, who was initially on the run, had been initiated.
About an hour later he came to the police station on his own.
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Two women are stabbed to death in a house and a third is injured.
On the balcony, a man shoots people with a crossbow.
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Almelo: Suspect seriously injured when arrested
The exact background to the crime and the motive are the subject of the ongoing investigation, the spokeswoman continued.
It was initially unclear whether and how the suspect commented on the allegations against him.
dpa