chk-remote-mountpoint /my/path/to/folder

df -P -T /my/path/to/folder | tail -n +2 | awk '{print $2}'

$ stat --format=%m /usr/src/linux
/usr/src

$ stat --file-system --format=%T /usr/src/linux
reiserfs

if mount | grep -q "/mnt/mountpoint" ; then
  echo "mounted"
fi

if mount | grep -q "/mnt/mountpoint" | grep -q nfs ; then
  echo "mounted"
fi