First look here - St. Louis Lost Pets http://www.stllostpets.org/
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This site contains animals at STL City & County Animal Controls, Animal Protective Association (APA) and The Humane Society of Missouri. These are the four most likely places your animal will be held.
ST. LOUIS CITY
City of St. Louis Animal Care and Control - http://accstl.com/
Stray Rescue - https://www.strayrescue.org/
ST. LOUIS COUNTY
STL County A.C. http://www.stlouisco.com/HealthandWellness/AnimalCareControl
Bridgeton A.C. http://www.bridgetonmo.com/departments/police/patrol-division
Florissant A.C. http://www.florissantmo.com/topic/index.php?topicid=106
St. Ann A.C. http://www.stannmo.org/299/Animal-Control
If you live inside or near the city limits of a small city inside of St. Louis County that has their own police department, it is possible that they are holding your pet until they take it to STL County Animal Control or STL County A.C. picks it up from them. Call the police department and check.
People find animals and hold on to them hoping to find the owner. They post here on Craigslist, Facebook and a neighborhood only social platform called Nextdoor. You must be verified as living at your address to join Nextdoor.
Facebook Lost & Found Group for St. Louis:
Pet Rescues frequently take in lost pets.
Check https://www.petfinder.com or you can find Pet Rescues at your local Petsmart/Petco on the weekends