I don't recall any member of LE saying "there is no immediate threat to the public." But - I don't remember everything, so maybe that is out there somewhere (I'd like to see who said it and when).
What I do remember is the Delphi Police chief deflecting a question from the press about the community being in danger on the same day the girls were found by saying he thought people in Delphi are "smart enough to know what to do." The Carroll County Sheriff said that he doesn't want people in the county to live their lives in fear, constantly looking over their shoulders. To be honest I feel that these non-answers were aimed more at preventing hysteria or vigilanteeism in the community than speaking to the actual danger that existed.
Contrast that to these statements which paint a different picture - these span the time period from immediately after the bodies were found up until the three year mark:
"
Be cautious and careful and be parents...know where your children are and what they are doing."
ISP: Delphi Amber Alert wouldn't have helped
Detective Kevin Hammond: "Things have changed for us all...
I am more vigilant with my own children since this happened."
The best of humanity in the worst of times | Carroll County Comet/
Interviewer: "This community has never had a double homicide, Sergeant, from what I understand, and it has been years that Delphi, a community of 3000, has ever had a murder. What do you say to this community tonight because a...killer is on the loose, a double murderer?"
Sgt. Riley: "Well, we tell people,
like we've been telling people since this has all started, you need to be safe out there. We are working 24/7 to try to solve this
horrendous crime."
CNN.com - Transcripts
Three Years Later: Everything we know about the murders of Libby German & Abby Williams in Delphi
“
I can’t say there’s not a threat to the community,” Indiana State Police Sgt. Kim Riley told RTV6 at the time. "We have not caught the person yet. Is the person still in the community? We don’t know.”
"Be cautious and careful....know where your children are....I am more vigilant with my own children....you need to be safe out there....(and then, three years later) I (still) can't say there's not a threat." None of this adds up to "don't worry folks, there's no immediate threat." It's pretty much the opposite, to me.