Did you read your own link or just someone’s summary of it?
This is not the CDC’s own study–its one by David A Geier, Brian S Hooker, Janet K Kern,Paul G King, Lisa K Sykes, and Mark R Geier. They are affiliated with of The Institute of Chronic Illnesses Inc (14 Redgate Ct, Silver Spring, MD), Simpson University University of Texas Southwestern Medical Center at Dallas, 4CoMeD Inc, Silver Spring, MD, The Institute of Chronic Illnesses Inc., respectively, as your link clearly states. Incidentally, The Institute of Chronic Illnesses Inc seems to be located in a suburban house.
The only connection with the CDC is that the authors used the CDC’s VAERS database for vaccine adverse reaction reporting to do their study. Reports in VAERS are not subject to verification. This link discusses the problems with VAERS and, in particular, the problems with the Geiers’ use of VAERS.
Also, the Geiers are a case in which a bit of ad hominem is fair enough. You can read about them here. Mark Geier lost his medical license for giving the “chemical castration” agent Luperon to autistic kids without any sound rationale. David Geier is his son, who has no medical qualifications.