We report a two-step chemical vapor deposition (CVD) method for fabrication of hierarchical polymer-coated carbon nanotube (CNT) microstructures having tunable mechanical properties and accessible chemical functionality. Diverse geometries of vertically aligned CNTs were grown from lithographically patterned catalyst films, and the CNT microstructures were chemically functionalized via poly[4-trifluoroacetyl-p-xylylene-co-p-xylylene] made by chemical vapor deposition polymerization. The polymer coating conformally coated the individual CNTs and CNT bundles within the CNT "forest". The chemical structure of the polymer films was verified by X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). Simple control of the mechanical properties of the nanocomposite structures can be achieved by adjusting the deposition times during CVD polymerization. Increasing the polymer film thickness from 10 nm to 27 nm resulted in a change of the Young's modulus from 65 to 80 MPa. These values are substantially higher than the 36 MPa measured for the as-grown CNTs without polymer coating. The effect of the polymer coating in reinforcing the connectivity among CNTs within the structures has been understood using an analytical model. Finally, chemical functionality of the CNT composite structures after CVD polymerization was verified by a 4-fold fluorescence enhancement after binding of a dye to the coated CNT microstructures. This technique can be adapted to a wide variety of reactive coatings and facilitates attachment of chemical groups and functional nanostructures on the surfaces of the CNTs; therefore, this material could serve as a tunable platform for coupling mechanical and chemical responses in materials for environmental and biological sensing.