The Collaborative International Dictionary of English v.0.48:

Paddy \Pad"dy\, n.; pl. Paddies. [Corrupted fr. St. Patrick,
   the tutelar saint of Ireland.]
   A jocose or contemptuous name for an Irishman; -- usually
   considered offensive. [Obsolescent]
   [1913 Webster +PJC]

The Collaborative International Dictionary of English v.0.48:

Paddy \Pad"dy\, n. [Either fr. Canarese bhatta or Malay
   p[=a]d[imac].] (Bot.)
   Unhusked rice; -- commonly so called in the East Indies.
   [1913 Webster]

   Paddy bird. (Zool.) See Java sparrow, under Java.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Paddy \Pad"dy\, a. [Prov. E. paddy worm-eaten.]
   Low; mean; boorish; vagabond. "Such pady persons." --Digges
   (1585). "The paddy persons." --Motley.
   [1913 Webster]

WordNet (r) 3.0 (2006):

Paddy
    n 1: (ethnic slur) offensive term for a person of Irish descent
         [syn: Paddy, Mick, Mickey]
    2: an irrigated or flooded field where rice is grown [syn:
       paddy, paddy field, rice paddy]
    3: rice in the husk either gathered or still in the field