This is the first instance of women qualifying to adjudicate at the World T20.
While Cross has officiated at the Women's World Cup in 2000, 2009 and 2013, Polosak will stand in a global event for the first time when she oversees the New Zealand-Ireland clash at Mohali on March 18.
Polosok had become the first woman to officiate in a senior men's cricket event in October 2015 when she was the third umpire for a Matador BBQ's One-Day Cup.
The group stage of ICC World T20 2016 is set to start on March 15.