Officers were called to Green Park in Ossett after reports online suggesting that dogs were being poisoned.
The reports came after local vets said two dogs had become ill following walks in Green Park and one had then died.
A West Yorkshire Police spokesman said: "There have been some reports on Social Media regarding suspected poisoning of dogs in Green Park Ossett.
"We have contacted most of the vets in Ossett and also Richmond’s vets in Dewsbury. Apart from Richmond’s, the vets in Ossett were aware of the incidents but had not treated any suspected poisoned dogs.
"Richmond’s did confirm that they have had 2 dog owners / walkers attend at their surgery over the past few days with ill dogs and both said they had been walked in Green Park over the past couple of days.
"Sadly, one dog died, the other two were given treatment and we believe they are recovering well.
"This morning Richmond’s Vets have confirmed that they are awaiting test results to try and identify why the dog died.
"There is no evidence to confirm the location of these incidents.
"If anyone has any information or has knowledge of similar incidents, please contact your local police."