L6203 H-bridge output current rings in response to step input
Extracts from L6203 data sheet: -


  Although the device guarantees the absence of cross-conduction, the
  presence of the intrinsic diodes in the POWER DMOS structure causes
  the generation of current spikes on the sensing terminals. This is due
  to charge-discharge phenomena in the capacitors C1 &amp; C2 associated
  with the drain source junctions (fig. 14). When the output switches
  from high to low, a current spike is generated associated with the
  capacitor C1. On the low-to-high transition a spike of the same
  polarity is generated by C2, preceded by a spike of the opposite
  polarity due to the charging of the input capacity of the lower POWER
  DMOS transistor (fig. 15).




These spikes along with bad probing techniques can generate what you are seeing. You need to use this type of o-scope probing: -