We can’t know what’s going on, whether or not the family was told to remain quiet. Or how aggressively it seems to the family the case is being investigated.
It is, sadly, not that uncommon these days for the process to be slow-walked if the perp(s) identity is of the “wrong kind”, ie a POC or other “disadvantaged” group. And we do know that a liberal town all too frequently equals a liberal city administration and subsequently a liberal police force, even if it’s by an order of the mayor.
Time will tell us if these factors are in play.
I think we can safely assume the police shared info with the family on the condition that it remain confidential. In my 37 plus years of being involved in criminal law, I’ve never seen otherwise. The only times I can remember the police being ok with family sharing info publicly was when the police shared bogus information with the hope that the family would share it to misdirect the perp.