Storm drains are for the sole purpose of rainwater overflow. Dumping trash, pollutants and debris in the catch basins is illegal and is a federal violation of the Clean Water Act of 1972 as well as the City of Abilene Municipal Code. If it's a neighbor, they may not understand the catch basin's direct connection to local creeks. If you have an amicable relationship with him/her, it may be just a matter of informing and making them aware of its environmental impact.
If it is someone who you feel is knowingly violating and repeatedly dumping into storm drains, please contact the City of Abilene to report incidents of illegal dumping.