I've had people telling me that spinal tap can cause paralysis.. is it true?

Highly unlikely: A lumbar puncture (spinal tap, lp) is a very safe procedure when done correctly. A needle is placed in the lumbar region (low back). The spinal cord ends higher up in the spine in most people and it would be very difficult to injure directly. Technically, there are risks to any procedure, but in experienced hands the chances of a severe complication are exceedingly rare with lp.