Yes, reptiles in general shed salmonella particles in much the same way humans shed skin cells. They can get everywhere!
For this reason, it is important to always wash your hands after handling the red-eared slider turtle as well as any surface they've crawled across with soap and water. You should also wash any clothes that have come in contact with your red-eared slider turtle as well.
Remember that you can also easily be exposed to salmonella by cleaning the turtle's tank or changing its water. It is a good idea to use latex gloves while doing these tasks for an additional layer of protection.
The Centers for Disease Control and Prevention recommend that reptiles are not kept in homes that have children under the age of five. Younger children are especially susceptible to salmonella since they often put their hands in their mouths. Salmonella poisoning is also more serious if in a child under five years of age.
The elderly and others with conditions that cause them to have weakened immune systems should also be kept away from reptiles such as the red-eared slider.