We have performed optical investigations of layers formed by sheets of aligned multi-wall carbon nanotubes (MWCNTs). Nanotubes have extraordinary mechanical, electrical and optical properties when they are unidirectionally oriented. Free-standing CNT sheets drawn mechanically from vertically-grown MWCNT forests can be deposited on glass substrates, with nanotube bundles mostly oriented in the drawing direction. These CNT sheet layers have optical anisotropy, which can be detectable even for a single CNT sheet. We have studied the optical anisotropy in transmission, finding a similar value at different length scales indicating similarities in the orientational order of the nanotubes, thus preservation of their average degree of order. Finally, light transmission was observed when the samples were at 45 deg between crossed polarizers.