We present a distributed algorithm for finding a (1 + Ɛ)- approximation of a Minimum Connected Dominating Set in the class of Growth-Bounded graphs, which includes Unit Disk graphs. In addition, the computed Connected Dominating Set guarantees a constant stretch factor on the length of a shortest path with respect to the original graph and induces a subgraph of constant degree. The nodes do not require any positioning or distance information. The algorithm runs in O(TMIS+1/ƐO(1) ċ log* n)synchronous rounds, where TMIS is the time for computing a Maximal Independent Set (MIS) in the network graph. Using the fastest known deterministic algorithm for computing a MIS, the total running time is O((logΔ+1/ƐO(1)) ċ log* n), where Δ is the maximum degree of the network graph. If one allows randomization, the running time reduces to O((log log n+1/ƐO(1))ċ log* n) rounds.