The dog's 22-year-old owner, who asked not to be identified, said she was exercising her two dogs Luna and Choco at Polyantha Reserve in Apple Blossom Drive, Mirrabooka, just after 6:00pm on Wednesday.
"Within a split second Luna was on the floor, I thought she was just submitting, wanting to play," the woman said.
"The man's bent down, I didn't hear any snarls, growl, yelps or barks, I thought everything was fine."
She jogged up to the man to make sure her dog was not bothering his small, tan-colored dog.
She said he put his hood on and mumbled something incoherent before he walked away and broke into a run and jumped a fence.
"I picked her up and lay her on top of me and felt her heart and I couldn't feel her breathing, she was gone within seconds."
The woman rushed Luna to a nearby vet but she could not be saved.
She said her dog was gentle, and good with other animals. She's our little baby, she sleeps on the bed with me … she was just beautiful," she said.
"Anyone who knew Luna would not say a bad thing about her. Every dog she met she loved, big or small."
He was wearing long dark pants and a light brown zip-up hoodie.
Police said the man and the woman were the only two people in the park at the time of the incident, and they wanted to hear from anyone who may have seen the man.
Police also want residents with security cameras, whose homes surround the park, to check their footage for any images of the suspect.
The offence carries a maximum term of five years in jail.
'I heard screams'
Local resident Tony was walking towards the park on Wednesday evening and heard yelling.
"I heard screams, what sounded like a young lady, it was a bit hard to see in the dark around about 6 o'clock," he said.
"Then I saw a car arrive, it seemed to be driving erratically and a lady got out of the car and went over to the person that had been screaming in the park.
"The person who was screaming seemed quite distressed."
Tony said he never walked through the park after dark, and used the path around the edge.
"I don't want to walk in this park after dark because you just don't know what could happen and there's no lighting in the park," he said.
(ABC - May 19, 2017)