Call the WDFW regional office and ask for contact information for the district wildlife biologist for the county where you saw the deer. They will know who has conducted radio telemetry studies of deer in that area in the past decade; it is very helpful to note all identifying marks (species, sex, color of transmitter and neck band, ear tags - colors and numbers).
Keep in mind radio collars last a lot longer than batteries - that collar can easily be 10+ years old on a deer, sheep or goat, 20+ years on an elk. Some herds have been studied several times during that interval (i.e., Chelan Co. mule deer), so you may not be able to determine which study the deer is from unless you can see some identifying mark.