The recent arrest of Golden State Killer suspect, Joseph James DeAngelo, was made with evidence found using a currently undisclosed Genetic method. It is confirmed however that GEDmatch, a public genealogy database was used to connect the crime scene evidence to relatives of Mr. DeAngelo. The article further discusses the difference between STR, or short tandem repeats, and SNPs, single nucleotide polymorphisms, when it comes to identifying individuals. There are only 20 STRs compared to 600,000 SNP so the possible combinations with SNPs is so much higher and allows investigators to determine not only familial ties but also the exact relation of two people.
Aside from the speculation of the methods used by police to identify DeAngelo from GEDmatch's data there are also concerns of privacy invasions and "genetic stop and frisks". If Police have access to DNA databases outside of their own central database of criminals they could theoretically start trying to connect people to crimes with no probable cause simply if their DNA matches closely enough. Granted the odds of two people having the same DNA sequence is incredibly low it is still technically possible and can result in arrests or questioning that otherwise would be unwarranted.
In my personal opinion the idea of genetic stop and frisks and police having access to public DNA records. The chances of a false match with current DNA procedures is so infinitesimal that it isn't really a good argument to be used against genetic profiling. The privacy concerns may be important to some people but I personally am not concerned with it as it is a small price to pay in order to make improvements to solving and ultimately stopping crimes.
Article 1 - https://www.sciencenews.org/article/golden-state-killer-suspect-dna-genetics-genealogy
Article 2 - https://www.washingtonpost.com/local/public-safety/to-find-alleged-golden-state-killer-investigators-first-found-his-great-great-great-grandparents/2018/04/30/3c865fe7-dfcc-4a0e-b6b2-0bec548d501f_story.html?utm_term=.16c7e578655d