Casey was at bat. He walked east on the conveyor belt as it rolled west. The belt carried packages, boxes, rolled-up newspapers -- just the sort of flotsam that would drift past on a similar belt in a post office.

Casey sniffed each piece of "mail" as it passed. But he didn't pounce. Not yet.

Finally, 11 weeks of training paid off. A carton marked "Campbell's Split Pea Soup" trundled past, and Casey lunged. As his handler, Morris Berkowitz, shouted praises at him and cuffed him affectionately on the neck, Casey sank his teeth into the box and started chewing it to bits. Another stash of dope--in this case, a small clump of marijuana stuck in the carton -- had been identified, by another dog working for Uncle Sam.

Casey is an 18-month-old German shepherd who completes basic training tomorrow at the U.S. Customs Canine Enforcement Training Center near Front Royal, Va.

Casey and five classmates will ship out over the weekend for the docks of Baltimore, the postal handling areas of Los Angeles International Airport, the immigration booths at Laredo, Tex.--anywhere illegal drugs cross a United States frontier.

Unlike the baseball variety, the drug-sniffing Casey is expected to bat 1.000. Customs evaluates 43 dogs for every one that graduates from its training facility, which sprawls across the grounds of a former farm just 200 yards from the Skyline Drive. Only 300 dogs have graduated in 13 years of continuous training.

Which dogs make it? "The ones that have that super retrieving desire," said Chuck Caldwell, an instructor and course developer at the training center. "This definitely isn't for just any dog."

Interestingly, many of the dogs now serving at Customs installations around the country came from that capital of Tough Times, the South Bronx. They were strays picked up by New York City animal shelters.

"I think they learned to concentrate very hard on one thing," said Caldwell. "Up there, it was surviving. With us, it's finding drugs, no matter what steps the smugglers take to conceal them."

The Customs Service will accept potential drug-sniffers from private individuals. However, officials emphasize that an owner must be prepared to give up his pet until the dog is at least nine years old. Officials also say that many dogs who fetch up a storm in a suburban back yard prove to be much less adept once they reach Front Royal.

"Take them out of the environment they know, and they'll look at you as if to say, 'What do you mean, chase that ball?' " Caldwell said. "A lot of people who give us dogs don't believe it. They can't believe their Rusty wouldn't perform. But it's the truth."

Still, you never know when a Rusty might turn out to be a Casey. So the Customs Service has issued a call to private citizens who own a sporting breed dog (preferably a shepherd, golden retriever or labrador retriever) no older than 18 months. If you can bear to part with your pet, the Customs Service can use him in the uphill battle against drug smugglers. And if Customs flunks the dog, he will be returned to you at government expense.

It's certainly a worthy cause. Customs dogs recovered $189 million worth of drugs in fiscal year 1981. If the number of dogs on duty doubled, that total probably would, too.

If you are interested, call 566-8188. And don't worry about what rigorous training will do to your pet. They say dogs can't smile, but when Casey got off that conveyor belt the other day, he sure wasn't crying.