The connection between the hamstrings and the sacroiliac joint is through what is known as the superficial back line myofascial meridian/anatomy train. If the hamstrings are tight, their tension pulling force will be exerted through the sacrotuberous ligament and onto the sacrum.
The coccygeus and levator ani are technically muscles of the pelvic floor, however, they are also muscles whose contraction forces cross the sacroiliac joint and therefore often tighten when a sacroiliac joint condition exists. The coccygeus attaches from the sacrum and coccyx to the ischial spine of the pelvic bone.
Even when the original reason for the sacroiliac stabilization is valid, often the human body overdoes it and tightens the musculature excessively and/or keeps it tight long after it needs to be, so the musculature becomes stuck in a chronic pattern of hypertonicity.
No assessment procedure is more important to the manual therapist than bone and muscle (myofascial) palpation.