The links of many medical-biological events with high levels of geomagnetic activity (GMA) are widely discussed. In recent years, several medical phenomena were described in inverse distribution by time with GMA. Also a concurrent to GMA and solar activity force-cosmic ray activity (CRA) and closely related high energy neutron and proton fluxes are studied as a forces dominating at low GMA and solar activity in relation to considered medical events. The aim of this study was to explore the distribution of some important medical events on days with "Zero" GMA levels, accompanied by high CRA (neutron activity). Medical event data of the Grand Baku region (more than 3 mln inhabitants), Azerbaijan, with daily distribution on the time 1 Dec. 2002-31 Dec. 2007 was compared to daily GMA Kp indices in general (Kp > 0, 1837 days) and 34 days daily GMA indices Kp = 0. Daily CRA data was also compared using neutron monitoring data from two stations. Daily averaged data and their standard deviations on the mentioned GMA levels were compared and statistical significance was established. Results revealed a significant rise in the number of emergencies (n = 1,567,576) and total deaths number (n = 46,360) at the days of "Zero" GMA level. These days were accompanied by significant rise of CRA (neutron activity). For Sudden Cardiac Deaths (SCD, n = 1615) and cerebral stroke (CVA, n =10,054) the increase achieved strong trend to significance level. Acute Myocardial Infarction occurrence (morbidity) and trauma were also absolutely more registered at days with "Zero" GMA level, despite the small number of such days. The average Infection numbers show an inverse relationship with absolutely high registry at the "Zero" GMA level days. Study linking environmental physical activity levels and the human medical data shows that geomagnetic field variations accompanied by the increased level of cosmic ray activity, can have either direct or indirect adverse effects on human health and physiology, even when the magnitude of the geomagnetic field disturbance is extremely small or even is equal to zero. On days of "Zero" daily Kp indices describing Geomagnetic Activity, accompanied by high Cosmic Ray Activity (neutron activity), more medical emergencies and total death number (daily) occurred. Sudden Cardiac Deaths and Cerebral Stroke numbers show a strong trend to significant rise. Absolute increase of number of Acute Myocardial Infarction and less Infections, not achieving statistical significance, was also observed. These results are additional data for considering Cosmic Ray Activity (neutron activity) as an additional factor involved in time distribution of human medical events.