Calcium levels and nerve hyperexcitation
From Uptodate on Clinical Manifestations of Hypocalcemia:


  Acute hypocalcemia directly increases peripheral neuromuscular irritability [ 1 ]. As measured electromyographically, tetany consists of repetitive high-frequency discharges after a single stimulus. Hyperexcitability of peripheral neurons is probably the most important pathophysiologic effect of hypocalcemia, but hyperexcitability occurs at all levels of the nervous system, including motor end-plates, the spinal reflexes, and the central nervous system.


Guyton and Hall Textbook of Physiology:


  The concentration of
  calcium ions in the extracellular fluid also has a profound
  effect on the voltage level at which the sodium
  channels become activated. When there is a deficit of
  calcium ions, the sodium channels become activated
  (opened) by very little increase of the membrane potential
  from its normal, very negative level. Therefore, the
  nerve fiber becomes highly excitable, sometimes discharging
  repetitively without provocation rather than
  remaining in the resting state. In fact, the calcium ion
  concentration needs to fall only 50 per cent below
  normal before spontaneous discharge occurs in some
  peripheral nerves, often causing muscle “tetany.”This is
  sometimes lethal because of tetanic contraction of the
  respiratory muscles.
  
  The probable way in which calcium ions affect the
  sodium channels is as follows:These ions appear to bind
  to the exterior surfaces of the sodium channel protein
  molecule. The positive charges of these calcium ions
  in turn alter the electrical state of the channel protein
  itself, in this way altering the voltage level required to
  open the sodium gate.