Redford has been silent since she resigned as premier three weeks ago, and has not been in the legislature to represent her riding of Calgary-Elbow.
However, on Thursday she began tweeting as a member of the legislature.
Her first tweet talked about how she is excited to have Stephen Colbert replace David Letterman as host of TV's "Late Show."
A second remark included a picture of her handing out grant money in Calgary to a community group that supports entrepreneurs.
Another updated her 36,000 Twitter followers on a meeting with a constituent on school issues.
A spokesperson in Redford's Calgary office said she was "not available" for interviews but declined to provide a reason.
Opposition members have said Redford needs to get back to the legislature to carry out her duties.
Premier Dave Hancock, asked about the legislature absences, said he plans to give Redford some room.
"One of the things that I think is important from my perspective is to not impose myself on her, her life, or how she carries out her role as an MLA," said Hancock.
"I wouldn't do it for anyone else, and I shouldn't do it for her."
NDP Leader Brian Mason said Redford deserves some space for now.
Redford stepped down ahead of a caucus and party revolt over her lavish spending and accusations of heavy-handed, top-down management.
"I think we should cut her some slack," said Mason.
"She's had a very rough period of time, a very rough go and I don't think we should expect to see her around here for a little while.
"Having said that, it's two years to the next election and it's completely unacceptable that she would stay away (from the legislature) for that length of time."
Under the Legislative Assembly Act, MLAs can be absent without from the house without good reason for 10 sitting days in a session before they are docked pay.
Legitimate excuses include government work, health, and bereavement.
For each day’s unapproved absence, MLAs are docked $100, plus $50 from their expense allowance.
The MLA base pay is $156,000.
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