No, there are no steroids in Spiriva®. Spiriva contains only one medicine, tiotoprium, which is a long-acting compound that opens up the tubes in the lung by relaxing the smooth
muscles found in the respiratory tract.
A number of inhaled medicines including the brand name products Advair® and Flovent® do contain a steroid which reduces inflammation when inhaled into the lungs. Inhaled steroids work directly in the lungs but there is the possibility of experiencing steroid side effects in the body. The side effect that is of greatest concern is reduction of bone strength which can lead to osteoporosis and fracture.
I do want to point out that the types of steroids that are in inhalers are not the same type of steroids that athletes sometime use to get bigger and develop stronger muscles.