Do I have the legal right to sue the hospital if my husband escaped suicide watch?

You can sue the hospital for negligence.  Negligence is the failure to exercise due care (that degree of care that a reasonable hospital would have exercised under the same or similar circumstances to prevent foreseeable harm).

When your husband is located, if he has been injured, he could recover compensation for the medical bills and compensation for pain and suffering in a lawsuit for negligence against the hospital.  Compensation for the medical bills is straight reimbursement.  Compensation for pain and suffering is an amount in addition to the medical bills.

Prior to filing a lawsuit against the hospital, it may be possible to settle the case with the hospital's insurance carrier.  Your husband's claim filed with the hospital's insurance carrier should include the medical bills and medical reports.  The medical reports will be used to determine compensation for pain and suffering.  If the case is settled with the hospital's insurance carrier, NO lawsuit is filed.  If yoru husband is dissatisfied with settlement offers from the hospital's insurance carrier, reject the settlement offers anf file a lawsuit for negligence against the hospital.  If the case is NOT settled with the hospital's insurance carrier, the lawsuit for negligence against the hospital must be filed prior to the expiration of the applicable statute of limitations or your husband will lose his rights forever in the matter.