Detectives believe the blood belongs to the man wearing the hat, rather than a young child, but have appealed for more information.
The baby sleepsuit was discovered on 10 March, but the latest find could help end the mystery of how it became covered in blood.
Detective Inspector Richard Baird said: “Following an earlier appeal in relation to the bloodstained baby grow, a member of the public responded to this and contacted Police Scotland to report he had heard a noise outside an address in the Lundavra Road area of Fort William.
“A man had been seen sitting in a garden between 8-9pm on the 10 March 2014 where the following day a blood stained adult size baseball cap was found.
“The cap is described as an Adidas Essentials 3 Stripe peaked cap, dark grey in colour with three yellow stripes on the peak.
“Following forensic examination I can confirm that the DNA from the blood on the cap is the same as the DNA from the blood on the baby grow. It is assessed that this DNA has come from the man wearing the cap.
“I am appealing for the owner of the cap to come forward, or persons who may know who he is, to contact the Police so that we can establish how he came about the injury.
“There could be a number of explanations of how this man came to be injured and Police are keeping an open mind regarding this.”
Police are keen to speak to anyone who has any information about the incident and would encourage them to contact Police on 101 or Crimestoppers anonymously on 0800 555 111 or online at crimestoppers-uk.org.