The Collaborative International Dictionary of English v.0.48:

Berretta \Ber*ret"ta\, n. [It., fr. LL. birrettum, berretum, a
   cap, dim. of L. birrus, birrum, a cloak to keep off rain, cf.
   Gr. ? tawny, red: cf. Sp. birreta, Pg. barrete, and E.
   Barret.]
   A square cap worn by ecclesiastics of the Roman Catholic
   Church. A cardinal's berretta is scarlet; that worn by other
   clerics is black, except that a bishop's is lined with green.
   [Also spelt beretta, biretta, etc.]
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Biretta \Bi*ret"ta\, n.
   Same as Berretta.
   [1913 Webster]

WordNet (r) 3.0 (2006):

biretta
    n 1: a stiff cap with ridges across the crown; worn by Roman
         Catholic clergy [syn: biretta, berretta, birretta]