Yes, there is a street route of about 18 blocks.  From the Katy Depot head (mile marker 227) directly east to fourth street, follow Fourth Street (approximately 5 blocks) to Engineer Street, turn left (north) on Engineer Street, follow Engineer Street (approximately 4 blocks) to Boonville Street, turn right (east) on Boonville Street, stay on Boonville street (approximately 9 blocks) past Heard Ave and you will turn left (north) onto the Katy Trail again.