TALLAHASSEE (CBSMiami/AP) – Five months after Jennifer Carroll abruptly resigned as lieutenant governor, Rick Scott is moving slowly to replace her.

Carroll resigned after she was questioned by law enforcement authorities about work she did for a charity accused of running an illegal gambling ring.

READ MORE: Sea Turtle Nesting Season Begins March 1 In Broward County

Carroll has not been accused of any wrongdoing.

But since March, the Republican governor has focused on other functions of his job instead of searching for a second-in-command.

READ MORE: 'Hot Mom' Says Catholic School Expelled Her 3 Kids Over Her Online Adult Videos

That opened Scott up to critics who say he has a duty to appoint a lieutenant governor.

Florida’s constitution says there “shall” be a lieutenant governor, but there is nothing in state law that says how quickly the governor must appoint someone. Constitutional scholars say it is unlikely any court would order the governor to act.

MORE NEWS: Stimulus Check Update: Why Your Next Relief Payment May Not Be $1,400

(TM and © Copyright 2013 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2013 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)