Parks had been arrested on March 31 last year on misdemeanor charges of harassment and family-offense domestic violence after an alleged incident involving a former girlfriend.
The former girlfriend was subpoenaed for the trial but did not appear to testify, leading the case to be dismissed by the DA's office.
In the arrest affidavit, Parks' former girlfriend stated that Parks had made threatening phone calls after a relationship ended. Parks initially told police he believed the woman had stolen items from his home.
Parks is still subject to discipline under the NFL's personal-conduct policy.
Parks, 23, has played in all 32 games since the Broncos selected him in the sixth round of the 2016 draft. He started five games last season and registered an interception, 4 passes defensed and 47 tackles.
ESPN's Jeff Legwold contributed to this report.