Several thousand Fairfax County residents who have not filed personal property declarations on their automobiles are receiving notices from the county's supervisor of assessments.

The county has obtained from the State Department of Motor Vehicles a computer listing of all vehicles registered at addresses within the county as of Dec. 31, 1981. The county is comparing that list with its file of vehicles on which personal property declarations have been filed for 1982 to identify those that have not been reported to the county this year.

Personal property tax declarations should have been filed by May 1. There is a late filing penalty of 10 percent of the tax due or a minimum of $5.

The Office of Assessments has begun mailing forms to people in Fairfax County whose autos are registered with the state but for which they have not filed personal property returns. A letter of instructions will accompany the personal property form.

In cases where the computer match process identifies vehicles on which personal property has not been declared, a follow-up will be made by the Office of Finance to determine whether the owners obtained county automobile tags.

The fee for county tags is $25 annually for motor vehicles weighing more than 4,000 pounds and $20 for smaller cars. There is no administrative penalty for late purchase of county tags, but operation of a vehicle on which the county tag fee has not been paid is a misdemeanor punishable by a fine of up to $100.