Thomas Eoannou told reporters that he would be calling for an independent investigation into how the supposed breach could have happened, but police said all evidence connected to the case is accounted for and intact.
"Hopefully they get the bottom of how this bag got open, by whom, and when, where the real evidence is, and it is established why anyone would have an incentive to tamper with a rape kit," Eoannou said.
Speaking at a news conference, he held up a plastic bag that contained what looked to be another bag.
"We know this to be the evidence bag that once contained the rape kit evidence. We know this because the bag has a label on it. It contains my client's identity," said Eoannou. "It is authentic."
Police in Erie County, New York, issued a statement defending the integrity of the evidence.
"All evidence related to this case that was given to Erie County Central Police Services by the Town of Hamburg Police Department is accounted for and remains in its original packaging in the possession of Erie County Central Police Services," said Erie County Police Commissioner John Glascott.
Erie County Central Police Services is an administrative agency meant to provide centralized support to the county.
"This includes the evidence in the rape kit and the packaging itself. This evidence has been analyzed and reports of that analysis sent to the appropriate agencies," Glascott said.
When sought for comment to respond to Glascott's statement, Eoannou could not be reached.
Police in Hamburg also did not immediately respond to a request seeking comment on the lawyer's allegation.
They did post a message on Facebook, however, saying that they would cooperate with any authorized investigation on the handling of evidence.
"That said, the Hamburg Police Department has documentation that unequivocally demonstrates that its handling of the evidence and the integrity of its chain of custody of evidence in this case is unassailable," the message read.
Police have previously said they were investigating an incident that allegedly occurred at Kane's home in early August.
"At this time, we are gathering information and awaiting forensic testing results," Chief Greg Wickett said last month.
He declined to answer a reporter's question on whether the case had anything to do with rape or sexual assault.
Kane denies wrongdoing
Kane has not been charged, and both he and his attorney deny any wrongdoing.
"My client maintains his innocence. So far, everything that we've been given from a physical evidence standpoint is consistent with what he says, and not consistent with forcible intercourse," said Paul Cambria, Kane's lawyer.
He told reporters Wednesday that he'd been told Kane's DNA was not found on the alleged victim "from the waist down."
"We're happy with the results. We don't want anything to be compromised, and obviously would have no incentive to participate in compromising it," he said.
"To me, if you don't like the results, now you start the smoke, and that might just be what this is," he said about the purported evidence bag that wound up at the home of the accuser's mother.
Kane plays for the Chicago Blackhawks of the National Hockey League. The team has so far supported him, allowing him to attend training camp.
He addressed the allegations against him at a news conference last week.
"This has been an incredibly difficult time for many people. I cannot apologize enough for the distraction this has caused my family, my teammates, this incredible organization, and of course our fans," Kane said.
"While I have too much respect for the legal process to comment on an ongoing matter, I am confident that once all the facts are brought to light, I will be absolved of having done nothing wrong."
Kane was drafted first overall by the Blackhawks in 2007 and scored a game-winning goal in a shootout in his first NHL game.
Arguably his most notable moment came in 2010, when he netted the Stanley Cup-winning overtime goal in Game 6 versus the Philadelphia Flyers to clinch the team's first championship in 49 years. Kane has since led Chicago to two more Stanley Cup wins, in 2013 and 2015.
He's also played in the Olympics, including the 2010 Games in Vancouver where he helped Team USA win a silver medal.
Kane remains a hugely popular player. His #88 jersey is the top selling customized jersey at the official NHL online store.
Blackhawks President John McDonough said the organization "prides itself in trying to make calculated and deliberate decisions based on information that we have at the present time."
At the same time, it recognizes Kane is "dealing with a very serious situation."
"We have the utmost respect for the legal process and will have no further comment on this issue at this time," McDonough said last week.