The science is not settled.

In 2012, the Institute of Medicine published, Adverse Effects of Vaccines: Evidence and Causality (2012).
http://books.nap.edu/openbook.php?record_id=13164

As detailed in this 894 page report:

158 adverse event-vaccine (AE/v) combinations were
studied. According to IOM, the evidence:


Convincingly supports a causal
relationship in 14 AE/vaccine relationships


Favors acceptance of a causal
relationship in 4 AE and vaccine relationships


Favors rejection of a causal
relationship in 5 AE/vaccine relationships (note: this includes MMR-autism)


Inadequate to accept or reject: 135
AE/vaccine relationships (85%)

The US govt is expanding the Vaccine Injury Tables based on 2012′s findings. Here is detailed background (28 page PDF) http://t.co/iOGLZznW. Note that the Chief
Medical Officer of the Vaccine Injury Compensation Program (VICP) asked for
autism to be listed as a “secondary cause” of vaccine injury in 2012
(see page 8 and 9 of the report at hrsa.gov/vaccinecompensation/iomreportupdate030812.pdf).
As of this writing the updates have not yet been finalized.

Shortly after this pivotal report, the Committee on
Assessment of Studies of Health Outcomes Related to the Recommended Childhood
Immunization Schedule commissioned a revised paper from a consultant, Martin
Kulldorff, Ph.D., titled, Study Designs for the Safety Evaluation of Different
Childhood Immunization Schedules. Many Vermonters provided public comment into
this process. See: Opportunity for Public Comment.

Following three information meetings, the committee
published their findings in, The Childhood Immunization Schedule and Safety:
Stakeholder Concerns, Scientific Evidence, and Future Studies (2013).

This report clearly states that,

“Few studies have comprehensively assessed the association between the entire immunization
schedule or variations in the overall schedule and categories of health outcomes, and NO STUDY has directly examined health outcomes and stakeholder concerns in precisely the way that the committee was charged to address its statement of task.”