Under my 1999 Suzuki Vitara in front of the transmission pan there is a small black plastic door.That is where the leak is coming from. l think that is where the torque converter is. Is the plastic door suppose to be loose?Would it leak if l overfilled it?

No it is not suppose to loose. If l remember right that is were the torque convertor is and it will leak on some cars if filled to high.

The plastic door u r referring to is the inspection cover, & u should be able to remove it. l do not know how loose it is & that would be a relative term, but as long as it stays in place then it is doing it is job. If the fluid that is coming out of that area is red, like transmission fluid, then the leak is coming from the front transmission pump seal. If it is oil, then the leak is coming from the rear main oil seal. Either way means removal of the transmission, & l would recommend replacing both seals at the same time.

Mtech is right, regardless if it is trans leak or rear engine seal, it will be major job.

So what color was the fluid? Many times a trans shop can do both cheaper than a regular shop.