Unfortunately there is no built in support for recording to a video file on the SD card. There are two camera data streams available: one for taking still pictures and one for showing a preview video like you have in a "regular" digital camera. No support for actual video recording.
Now, it doesn't say exactly what your project is supposed to do or what you want to use the video for, but perhaps it would be possible to generate the actual video file as a post processing step? This might work If you don't intend to use the actual video file on the Spresense board itself after recording. In that case you could save the frames from the preview video as separate image files on the SD card instead of displaying them on a display etc. Then, when the recording is finished, plug the SD card into your PC instead and combine them into a video file using an external tool such as ffmpeg.
This workaround might not work for you - it depends on what you want to accomplish - but it is the simplest solution I can come up with.
I found this similar thread that might be interesting to you: