Rosemary is an evergreen small woody plant that belongs to the mint or sage family. It is native to Mediterranean area but has been naturalized in many places as a culinary herb, for rosemary extract and decoration purposes.
It has a pungent, somewhat bitter taste with a characteristic aroma and often used sparingly as a flavoring or for food seasoning. Both dry and fresh leaves are used in dishes including soups, turnips, chicken, duck, lamb, seafood, potatoes, stuffing, and so on.
Can dogs eat rosemary herb?
Yes. Dogs can eat rosemary sparingly or in small amounts occasionally or as directed by your veterinarian. Fresh or dried leaves and twigs are safe for these pets
You can chop and add it to their food, use it to make herbal tea, or use it as an ingredient for its treatment or in its water. It can also be mixed with other safe herbs including thyme, dill, basil and so on.
There even commercial products like Zoe Pill Pops for Pets, Healthy All Natural Dog Treats for Giving Medication with the roasted chicken in rosemary.
a). Is the extract safe for dogs
Yes. Rosemary extract is safe with no genotoxic risk since the concentration of the essential oil is low owing to the method of extraction employed. It is often added to pet foods as a preservative to increase shelf-life.
Therefore, you do not need to go for wet or dry rosemary free dog food (without this herb or extract). Rosemary extract in dog food is totally safe.
b). The essential oil
Rosemary essential oil is listed among those not safe for dogs together with tea tree, clove, juniper, garlic, thyme, oregano, and wintergreen. 
Similarly, as VetriScience Laboratory notes, “very high doses of rosemary essential oils have shown the potential for toxicity problems for pets and humans.”
Do not use it on dogs that have a history of seizures. In fact, it is best to avoid it completely including its topical use as these pets may lick it afterward.
Is rosemary bad for dogs or good?
Besides being a flea, tick or bug repellant, according to Rover.com, it “contains antioxidants that may prevent cancer and heart disease and is good for your dog’s digestive.” It will deal with indigestion, gas, and other digestive issues.
Secondly, it will support a healthy heart because Dog Naturally states, has “antispasmodic (spasm preventing) abilities on smooth muscles. Rosemary can also help the heart in some cases of cardiac arrhythmia, as well as to generally strengthen the heart.”
In addition, it will boost your canine friend’s memory and improve its mood since it has a relaxation or calming effect. There is a link between dog epilepsy and rosemary since excessive amount may work as a brain stimulant rather than a calming agent worsening some of the existing nervous disorders such as epilepsy.
Moreover, its antimicrobial properties make it be used on dog’s skin in case of minor bruises or injuries, in eyewashes for minor eye infections or in treating some UTIs.
Finally, still on dog skin, it will ensure a glossy coat. You need to make its herbal tea (use a teaspoon of ground dried rosemary in about 500ml of hot water). Strain it and once it cools, use it as a final rinse on your fluffy friend coat.
Benefits to humans
In humans, some of the benefits of this herb include improving brain function, stimulating hair growth, relieving pain and joint inflammation, easing stress, bettering blood circulation and digestion, getting rid of free radicals, among others.
Rosemary is not bad for dogs. However, ensure you give them only a small amount to avoid stomach upsets. While its extract is safe, avoid using its oil.
For dosage, discuss with your vet to help you come up with the right amounts depending on why you are using it.
Finally, like any other food or herb, it can cause an allergic reaction. In case of any signs of allergies, stop giving it to your canine friend. However, this does not mean that is harmful as the allergic reaction may be an isolated case.