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Police want to trace 20-year-old Alan Davies after the attack in Lye on 9 February.
Officers were called to the family home that evening after a man, believed to have been Davies, sneaked into the house through an open window and then launched an unprovoked attack on the 19-year-old woman inside.
The victim, who was known to the offender, suffered head and facial injuries, for which she received treatment.
Police now want to speak to Mr Davies in connection with the incident, however officers have so far been unsuccessful with attempts to trace him.
Detective sergeant Craig Harris, from Dudley Public Protection Unit, urged people to come forward and help trace Davies.
"We want to hear from anyone who knows where Alan is, as we need to speak to him as part of our investigation into this assault," he said.
"The victim’s injuries were fairly serious and we urge people to help us trace the suspect, where possible."
Anyone with information as to Mr Davies’ whereabouts is urged to contact Dudley PPU by dialling 101, or speak to Crimestoppers anonymously on 0800 555 111.