HARTFORD, Conn. — The race is on for more gambling casinos in southern New England now that Massachusetts is jumping into the business.

Connecticut’s Mohegan Sun is seeking to build a casino in Palmer, Mass., as other casino developers look at Springfield and Holyoke as possible sites in western Massachusetts. Rhode Island voters will be asked next year to approve a ballot question on whether to turn a slot parlor into a casino.

Maine’s two casinos will soon introduce table games.

Massachusetts Gov. Deval Patrick signed legislation Tuesday authorizing up to three competitively bid casinos and one slots parlor.

Connecticut officials expect the competition will hurt business at the state’s casinos. Revenue already has declined because of the weak economy and competition.

In addition to western Massachusetts, eastern and southern parts of the state are authorized for casino construction.