By Roseanne Tellez

(CBS) – It’s been one month since the killings of six people inside a Southwest Side home. But are police any closer to solving this murder mystery?

CBS 2’s Roseanne Tellez reports.

Crosses and candles — now covered in snow — mark the loss of six members of one family, in a violent killing spree a Gage Park home.

Police say five of the victims were slashed by three different bladed weapons. The sixth, Hermina Martinez, was shot multiple times.

Police sources now say a domestic dispute related to Martinez is the strongest theory. Murder-suicide is least likely. There’s zero evidence it’s the work of a drug cartel, as rumored early on.

Meanwhile, robbery is unlikely since nothing was missing.

Despite no arrests one month into the investigation, police say they’re making progress. Video from nearby cameras has been of value. There is much DNA evidence to sift through, and cooperation from residents and family is described as immense.

The Mexican Consulate is serving as the go-between for family members in Mexico and police,  providing updates on the investigation and assisting with paperwork — even papers to get the family dog back to Mexico.