  We introduce the concept of 3-Lie-Rinehart superalgebra and systematically
describe a cohomology complex by considering coefficient modules. Furthermore,
we study the relationships between a Lie-Rinehart superalgebra and its induced
3-Lie-Rinehart superalgebra. The deformations of 3-Lie-Rinehart superalgebra
are considered via the cohomology theory.
