The Baltimore Gas and Electric Company says it is withdrawing the ''scratch and sniff'' cards it sent to 300,000 customers to alert them to natural gas odors after the effort led to false fire alarms.

''It is somewhat of a embarrassment,'' said a company spokesman, John Metzger.

The problem arose when the utility sent out its annual warning about natural gas in its ''Energy News'' brochure, which was mailed on Aug. 26 with electric bills, Mr. Metzger said.

On the back of the brochure was a drawing of a red flame and the words: ''Scratch this flame with your fingernail. Sniff it. Let your family sniff it and be sure everyone recognizes the odor.''

The scratch was to release the sulfurous rotten-eggs odor that is added to natural gas to alert customers to leaks. The highly flammable fuel itself is odorless.