The stretch reflex is the quickest neural loop in our body. If you strectch a muscle quickly this one contracts. It involves a sensitive neuron, an inter-neuron in spinal cord and a motor neuron.
But, this reflex is actually somehow contradicted since we feel the stretch and thus higher centres are certainly involved.
Corticospinal projections have an indirect role in stretch reflex. This is particularly evident in people with strokes affecting this tract. In them, the stretch reflexes are exaggerated. This is because the corticospinal projections provide an inhibitory drive to the stretch reflex preventing it from overcompensating for stretch and helps in smoothing the muscle contractions.