HPD found the mother, in her 20s, and her daughter, between 2 and 4 years old, dead in a third-floor apartment, after a family member of the woman flagged down officers in the area around 2:45 a.m.
Police said they found a man with blood on him in the apartment, and have identified him as a person of interest in the case.
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"As they arrived at the apartment, an occupant stepped out," HPD Assistant Chief J. Bryant said. "They immediately detained him because they noticed suspicious activity at the apartment."
Investigators aren't releasing much information about how the mother and daughter were killed why the man was with them.
However, police said they're not looking for anyone else connected with the two deaths.