Nalbandian was disqualified from the final at Queen's Club after kicking an advertising hoarding into line judge Andrew McDougall's leg during the second set against Cilic, causing an inch-long gash.
The Argentinian was fined the maximum penalty of 10,000 euros by the ATP and the Metropolitan Police yesterday [Tuesday] confirmed they were investigating a complaint of alleged assault against the 30-year-old Nalbandian.
Croatian Cilic, who was awarded the match following Nalbandian's disqualification, told The Tennis Space: "I was surprised when I heard that the police were getting involved because what happened on the court wasn't intentional.
"I mean, of course, it was just a reaction, but it ended up being quite tough for him finishing the match like that being defaulted. And then to confront this, with the police, that's pretty bad.
"I think it's an overreaction for the police to be involved. I don't really want to judge but he wasn't trying to do that intentionally, as he knew that if he did that he would be defaulted. I don't think he was trying to do anything like that."