"When the eight cats and Yorkshire terrier were thrown out the window, we were open," said Director Karen Josephson, "The person didn't even bother to come into the building and sign them over, so that's very disheartening."
A volunteer with the center followed the car and recorded the vehicle's Davidson County license plate.
Also Monday, shelter workers discovered two dogs sealed in a cardboard box with no food, water or air holes and a note that read, "Ate my chickens."
"The instant you see the animals are okay, then you get angry and you can't help it, you just have to bury it and keep going," Josephson told Nashville's News 2.
On Wednesday morning, workers witnessed another drop off outside the facility.
"We looked up and there was a woman dumping a crate upside down in the parking lot," said Josephson. "[She] dumped a cat out, jumped in her car and left."
Josephson added, "We always tell ourselves the economy is bad, people are struggling, but when this continues to happen, I can tell you it's because we lack a state law with any penalties, no animal law with any teeth and not anything that can be done on the county level."
The Montgomery County Animal Control facility can house about 90 animals, and lately, Josephson said they don't seem to empty out.
"We take in 25 [animals] a day, 7,000 a year, that's a lot of animals, a lot of unwanted animals," Josephson said, adding, "When you get in 25 to 30 [animals] a day, and you can only house 90, you do the numbers. You're full and you euthanize."