Carly Gregg, the 15-year-old girl accused of murdering her mother, is displaying some odd courtroom behavior ... getting a bad case of the giggles while sitting at the defense table.

Check it out ... the Mississippi teen was dressed in a conservative navy blue ensemble as her trial kicked off Thursday. Her defense attorneys flanked her on both sides, donning serious expressions during the trial ... though, Carly seemed to get a kick out of the proceedings, as she fought back some laughter.

While it's unclear what exactly prompted Carly's giggles, the video shows her female lawyer writing something on a pad ... which appears to be what sparked the shocking response from the teen.

Gregg is currently on trial for allegedly shooting her mother, Ashley Smylie, back in March ... when she was only 14 years old.

She is also accused of trying to kill her stepfather, Heath, who testified about the shooting this week.

Prosecutors played video footage they say shows the harrowing incident in court Tuesday ... and you can see Carly holding what looks like a handgun behind her back before strolling out of frame -- and gunshots are heard. Smylie was murdered with a .357 Magnum.

Gregg's legal team is pursuing an insanity defense after previously turning down a plea deal that would have likely landed the teen in prison for 40 years.

In addition to murder, Gregg has been charged with attempted murder and evidence tampering.