Yes. Either parent may sue for the child. However, there are particular requirements for how the lawsuit must be worded, and failure to comply with those requirements can be fatal to the case.
Importantly, the procedure for filing suit to recover for medical bills incurred by the parent or parents can be different from the action for injuries suffered by the child. Typically these two actions are combined in one lawsuit but not always.
Finally, different statutes of limitation can apply to each action—generally two years after the child reaches the age of 18 (the child’s 20th birthday) for the injury claim but only five years after the accident for the parent’s recovery of incurred medical bills if the parent pursues that claim separately. If this sounds confusing, it can be. For this reason, it is highly recommended that anyone pursuing a claim on behalf of an injured child be represented by an experienced attorney. Consult with an attorney early on in the process to avoid potential pitfalls.