A 52-year-old woman died at an address in Main Street in Buckton, near Bridlington, on Tuesday December 19.
A 56-year-old man was arrested in connection with the incident. He remains in custody and is being questioned by detectives.
Humberside Police officers are not looking for anyone else involved in her death and believe it is an isolated incident.
Detective Chief Inspector Mark Goulding from Humberside Police’s Major Crime Team said: “We have been undertaking a number of enquiries to ascertain the circumstances of the woman’s death and they are continuing today. As part of those enquiries we are continuing to question a 56 year old man arrested at the address yesterday and he is assisting with our investigation.
“We would like to reassure residents of this small community that at this time we are not looking for anyone else in connection with the woman’s death and we believe this to be an isolated, contained incident.
“My officers have been speaking to residents in the area following the incident. I would ask anyone who may not have spoken to us but who may have information they think relevant to the investigation to contact us on 101 quoting log number 481 of 19 December 2017.”