Many conventional medical monitoring devices, while not technically invasive, are nevertheless obtrusive insofar as they require contact with the patient. This obtrusiveness sometimes poses problems in daily clinical practice. The need for contact with electrodes or transducers is particularly relevant in the case of patients recovering in intensive care units where continuous monitoring is required, in turn requiring continuous direct transducer contact for prolonged periods. Among the many physiological parameters commonly acquired, the respiratory and the cardiac rates of the patients are of primary importance. Typically these two parameters are measured respectively using spirometry and electrocardiography (ECG), both involving obtrusive measurement systems requiring contact with the patient with an air conduit and electrodes. This paper presents an optical measurement method for the simultaneous assessment of respiration and heart rates based on the measurement of the chest wall movements, associated with inspiratory/expiratory activities of the lungs and by the mechanical pumping action of the heart. The measurement method has been adapted for use with preterm infants and it has been applied to 55 patients recovering in a Neonatal Intensive Care Unit. The method is based on the use of a laser Doppler vibrometer (LDVi) pointed at the left, ventral thoracic surface of the patient. LDVi-based measures of respiration and heart rate have been simultaneously acquired for each patient, in parallel with the same quantities acquired using conventional reference instrumentation (flow-meter and ECG) for comparison purposes. Results show that for respiration rate, differences with respect to the spirometer data are <3%, while for the cardiac rate they are <6% with respect to ECG data. The method proposed in this paper has the advantage of requiring no contact with the patient. Moreover, it supports, by means of a single instrument, the simultaneous measurement of respiration and heart rates, thus reducing the burden of the number of electrodes, transducers, and other instrumentation that must be applied to the patient--a consideration that is particularly important in the Neonatal Intensive Care Unit. In addition to the measurement of respiration rate, we also describe the sensitivity of the LDVi method in detecting key respiration events (irregular inspiration/expiration cycles, apneas, and hiccups) which are relevant to clinical monitoring.