LOS ANGELES — Ten years ago, Shirley Worthington rushed her dog Tigger to the vet when his mouth started bleeding. When she was told he had cancer, she knew to blame her heavy smoking — an addiction she still couldn’t kick until after her pet died.Secondhand smoke can cause lung and nasal cancer in dogs, malignant lymphoma in cats, and allergy and respiratory problems in both animals, according to studies done at Tufts University’s School of Veterinary Medicine in Massachusetts, Colorado State University and other schools. Although the number of pets that die each year from tobacco exposure isn’t available, vets know from lab tests and office visits that inhaling smoke causes allergic reactions, inflammation and cancers in pets, said Dr. Kerri Marshall, the chief veterinary officer for Trupanion pet insurance.Worthington, 52, of Brooklyn, N.Y., said she was a teenager when she started smoking and she had always smoked around Tigger, who was 8 when he died in 2004. A year later, Worthington, her mom and her sister all quit in honor of the bichon frise. Then, in 2007, Worthington’s mom died while suffering from cancer.“Cigarettes took my mother,” Worthington said. “And they took my dog.”Pets aren’t mentioned in this year’s surgeon general’s report, but in 2006, it said secondhand smoke puts animals at risk. The Legacy Foundation, the nation’s largest nonprofit public health charity, has encouraged smokers to quit for the sake of their pets, and the American Society for the Prevention of Cruelty to Animals urges making homes with pets smoke-free. It’s even more important to safeguard cats, experts say, because they are more susceptible to tobacco smoke than dogs. Lymphoma is one of the leading causes of feline death. Research at Tufts College that focuses on respiratory function in small animals shows that repeated exposure to smoke doubles a cat’s chances of getting the cancer, while living with a smoker for more than five years increases the risk fourfold. It can also cause a fatal mouth cancer. Tobacco companies acknowledge the risks of smoking in people but haven’t taken the same stance with dogs and cats. Philip Morris USA says on its website that it believes cigarettes cause diseases and aggravates others in nonsmokers, adding that the problems warrant warnings. But “we haven’t taken a stand on the potential impact on pets,” said David Sylvia, a spokesman for Altria Group Inc., the parent company of Philip Morris.Symptoms of cancer in animals include coughing, trouble eating or breathing, drooling, weight loss, vomiting, nasal discharge, bleeding and sneezing. Cancer kills more dogs and cats than any other disease, according to Denver-based Morris Animal Foundation, which has been funding pet cancer research since 1962.In addition, the recent surge in the use of electronic cigarettes has raised questions about their impact on pets. The greatest danger is the trash, where dogs can find nicotine cartridges from e-cigarettes, said Dr. Liz Rozanski, a veterinarian and researcher at Tufts.“You wouldn’t think dogs would eat such things, but they do,” she said.