Simply false. Here are studies which compare children given MMR to control children given no MMR vaccines. Both find no statistically significant correlation between MMR vaccine and autism:
http://journals.lww.com/pidj/Abstract/publishahead/Lack_of_A...
http://www.plosone.org/article/info:doi/10.1371/journal.pone...
There are also temporal studies comparing autism rates over time after the reduction/removal of thimerosal from vaccines (disproving a narrower hypothesis, that thimerosal causes autism):
Hviid A, M Stellfeld, J. Wohlfahrt, and M Melbye (2003). Association between thimerosal-containing vaccines and autism. JAMA 290:1763-1766.
Madsen KM, MB Lauritsen, CB Pedersen, P Thorsen, AM Plesner, PH Andersen, PB Mortensen (2003). Thimerosal and the Occurrence of Autism: Negative Ecological Evidence From Danish Population-Based Data. Pediatrics 112:604-6.
Fombonne E, R Zakarian, A Bennett, L Meng, D. McLean-Heywood (2006). Pervasive Developmental Disorders in Montreal, Quebec, Canada: Prevalence and Links With Immunizations. Pediatrics 118:e139-50.
Fombonne E (2008). Thimerosal disappears but autism remains. Arch. Gen. Psychiatry 65: 15-6.