Inclusive $D^*$ production is measured in deep-inelastic $ep$ scattering at HERA with the H1 detector. In addition, the production of dijets in events with a $D^*$ meson is investigated. The analysis covers values of photon virtuality $2< Q^2 \leq 100$ GeV$^2$ and of inelasticity $0.05 \leq y \leq 0.7$. Differential cross sections are measured as a function of $Q^2$ and $x$ and of various $D^*$ meson and jet observables.