Can the Nikon D3100 take still images while recording a video?

I was wondering if the Nikon D3100 can take images while recording videos, sort of like the Canon Rebel T3i.

No.

The only camera that can really do that now is the Nikon 1 series.

The adverts show that you can bull video captures from the video you have captured.

What you don't seem to understand that what ever camera you use to shoot video is capturing 24 to 30 frames per second and they are very reduced resolution, 1 mp for HD video and 2 mp for Full HD video.

The number of pixels your D3100 can capture as a still camera is 14 mp… A huge difference

I own a Canon t1i and it can do that… However it interrupts the video recording to take the shot.
Any dslr camera that does this will interrupt the video.