Rasmussen, 24, signed a one-year contract with the Blackhawks in June of 2014. He had 13 goals and 14 assists in 73 games for the Rockford IceHogs of the AHL last season. He was recalled by the Blackhawks in January, but did not appear in any NHL games.
Nordstrom, 23, had three assists and averaged 10:38 of ice time in 38 regular-season games and played in three playoff games for the Blackhawks last season. He also had nine goals and seven assists in 23 games for the IceHogs last season. He is coming off his three-year entry-level contract.
Carey, 23, signed a two-year contract with the Blackhawks as a college free agent in the 2013-14 season. He played two games for the Blackhawks in the 2013-14 season. He had 10 goals and 11 assists in 67 regular-season games for the IceHogs last season.
Carey and Rasmussen were among eight potential restricted free agents for the Blackhawks. The Blackhawks re-signed defenseman David Rundblad, who was set to become a restricted free agent, on Monday.