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A woman was found dead late Thursday in a Lakeville home, and police arrested a man in Rosemount about 40 minutes later in connection with the case, officials said Friday.

A family member alerted police at 11:10 p.m. Thursday about a "significant amount of blood" at a residence in a townhome complex just east of Pilot Knob Road, in the 17000 block of Encina Path, police said.

Officers arrived and found the woman's body inside. They have not disclosed how the woman was killed or why. Her identity was not released Friday.

A man was quickly identified as a suspect, and authorities issued an alert to law enforcement agencies to look for a specific vehicle.

About 11:20 p.m., a call to Rosemount police directed them to the 3700 block of 148th Street, nearly four miles from the scene of the death. Officers soon found the vehicle associated with the man, Lakeville police said.

A brief search about 11:50 p.m. led to the man's arrest nearby in a backyard, officials said. "He was found to have injuries that appeared to have been self-inflicted," according to a statement from Lakeville police. Emergency responders took the suspect to Regions Hospital in St. Paul, where he remained in custody while receiving medical attention.

Lakeville Police Chief Brad Paulson said Friday that police believed there was a family relationship between the victim, said to be about 30 years old, and the suspect, in his early 20s. Paulson said police were investigating who lived at the home on Encina Path and were not yet ready to release information on the weapon or weapons used.