In February this question was presented to the Carroll County Sheriff in a newspaper article and he answered thusly:
Q. Is there partial DNA or a full DNA profile of the suspect?
If there is DNA, has it been run against a genealogy DNA database?
A. This also speaks to an evidentiary aspect of the investigation.
So he elected not to answer the question, citing the integrity of the investigation.
Source:
County Sheriff answers double homicide questions from readers | Carroll County Comet
However, a few weeks later a documentary on the murders aired on HLN and he was asked if LE have DNA in the case and he answered that they do have DNA but they do not know if it's the killer's DNA.
We know that investigators in the Delphi case previously consulted with ex-criminologist Paul Holes, who was involved with the solving of the Golden State Killer case using genetic genealogy:
‘They Have A Tough Investigation Ahead:' Paul Holes On The Delphi Murders | Oxygen Official Site
IMO the only point in consulting with Holes specifically is to gain his perspective on genetic genealogy techniques. So from this we can guess that Delphi investigators hoped to use these methods or at least look into them. It should be noted that Holes believes, per that article, that their road will be a difficult one. This technique would be a legal strategy to pursue if the DNA Delphi investigators have is usable.
The other piece of info that pertains to this is that familial DNA searches in crime databases aren't legal in Indiana at this time. This is the method that caught the Grim Sleeper serial killer in California - investigators had unmatched DNA from his crimes and when his son was arrested for an unrelated felony, his DNA came back as a partial match for the Grim Sleeper. This told investigators that they needed to look at close relatives of the son as the contributor for the unsolved rapes/murders. This investigative method is allowed in about 15 states but Indiana is not currently one of them.