A beam of rovibrational energy level selected and magnetic state polarized ((X) over tilde)(1)A(1)) CD3I \JKM] = \111] was photodissociated at 266 nm. State-selective detection of the photoproducts allowed determination of elements of the transition dipole matrix or T matrix. We present here the methodology involved in the extraction of the T matrix elements from such quantum state-to-quantum state experiments and furthermore compare the results to cases where quantum and semiclassical descriptions are expected to be most accurate. A brief description of the effects of nuclear-spin depolarization on the accurate determination of the T matrix elements is also included. After depolarization is taken into account, the magnitudes of the T matrix elements for the R(Delta J = 1) and Q(Delta J = 0) product waves were 6.4 and 6.9, respectively, The relative phase between these waves was +/-11 degrees, which is due purely to the structure of the excited state potential surface, These T matrix values give a beta = 1.94 for the photodissociation of CD3I at 266 nm.