Karine Hakobyan, 38, was shot to death March 26 in the carport at her apartment complex, more than a year after her husband Khachik Safaryan, 43, and their 9-year-old daughter Lucine were killed in the family home on Dec. 11, 2008.
All three bodies were found by another daughter, who was 13 when her father and sister were killed.
Police were investigating whether Hakobyan or Safaryan were involved with an unidentified third party, Myers said.
He cautioned, however, that it was only one theory being investigated.
Myers said police have offered protective custody to the surviving girl and stepped up patrols in the Hollywood neighborhood where the mother lived.
The family was trying to establish a trust fund to support the girl, Myers said.
Hakobyan and Safaryan married in Armenia and moved from the capital city of Yerevan to the U.S. in 2003.