Actually, if you look at the history, China government has the final say on who will be the reincarnation of a high lama such as the Dalai Lama and the Panchen Lama. The selection procedure of the reincarnation of the high lamas was already formulated and decided on since the Qing dynasty. This procedure was also agreed by the Tibetans.
Since Qing dynasty, the selection of the reincarnation of the Dalai Lama or the Panchen Lama has to be supervised and approved by the Chinese government. How the Chinese government finds the reincarnation of the Dalai Lama or the Panchen Lama is according to the tradition, it is not what they have created.
If the CTA insists on finding their own Dalai Lama, they are going against the procedure. Their selection of the Dalai Lama will not be according to the tradition. If there are two Dalai Lama, the one picked by the Chinese government will be the legitimate one.