Willow Smith
Willow SmithWikimedia Commons/Joe Warminsk

Will Smith and wife Jada Pinkett Smith might have found nothing inappropriate in their daughter Willow Smith, 13, lounging on a bed with a shirtless Moises Arias, 20, but Los Angeles Child Protective Services is not taking the incident lightly.

The agency has reportedly launched an investigation, which is expected to last at least a month.

"The investigation was formally opened last week and is being taken very seriously by the department," Radar Online quoted an insider. "Will and Jada Pinkett Smith have been extremely cooperative with officials. Of course, they aren't happy that their parenting skills are under scrutiny, but they understand."

The Smiths are understood to have a liberal parenting policy, and they do not believe in punishing their children. The couple also believe in giving the kids as much control over their lives as possible. But that has only brought in more media scrutiny on Willow and Jaden Smith's behavior.

Last year, when Willow released the video for her "Summer Fling" song, her parents came under fire as the video showed her getting romantically involved with an older boy. Many also found her choice of clothes questionable and even criticised her for acting older than her age.

And regarding Willow's controversial Instagram photo, Jada went on record saying she did not find it inappropriate, and that the media should stop sensationalising it.

"Here's the deal," Jada told the media outside Los Angeles International Airport. "There was nothing sexual about that picture or that situation. You guys are projecting your trash onto it. You're acting like covert pedophiles and that's not cool."

The Radar Online source added that Child Protective Services will talk to Willow and Arias, before they conclude the investigation.

"Social workers will also be talking separately with Willow, and they also want to talk to the young man in the picture with her as well. This won't just be one or two visits with the family, and it will likely be an open investigation for at least a month, out of an abundance of caution."