Ingesting large amounts of a tomato plant's leafy greens or fruit blossoms may cause intestinal problems in dogs, but the ripened fruit itself presents no risk of harm. As long as sun-dried tomatoes are not packed in anything that will itself present problems to your dog, small amounts of this food will not cause any problems.
Sun Dried Tomatoes
Sun-dried tomatoes are first cured with sulfur dioxide or salt, then placed in the sun. Sulfur dioxide, in low amounts, will not cause any problems for animals. Salt can pose more of a risk, but only if your dog is getting it from multiple sources. The tomatoes themselves, selected at their peak ripeness, will have no stalks or stems and so will be extremely low in tomatine.
Alpha-tomatine is a substance present throughout tomato plants.The concentration of this substance is highest in the unripened fruit, blossoms and leafy greens. Tomatine can be toxic, but a dog would have to ingest a massive amount of tomato to be affected. Tomatine is poorly absorbed the intestinal tract and therefore poses minimal risk.
If the sun-dried tomatoes you have are packed with other ingredients, you may need to be careful about feeding them to your dog. Onions and garlic, for example, can cause hemolytic anemia in some Japanese breeds.
Sun Dried Tomato Treats
A variety of tomato-flavor dog treats exist in the pet trade, and some contain actual sun-dried tomato. You can make some yourself, too. Simply take any traditional dog biscuit recipe and include pieces of sun dried tomato in the mix. Ensure that the tomatoes you use are finely chopped and were packed in a substance that will not harm your dog. Your pet can eat sun dried tomatoes directly from the jar, but take care to feed only a small amount -- one every two or three days, max, unless you get the vet's approval.