How did police find Christians?

In episode 19 of the anime [Samurai Champloo], there is a scene where law-enforcement blockade a road and force everybody to step on a Christian symbol. If a person who steps on the symbol starts praying then the law-enforcement would arrest them for being Christian.

1. Did this method of finding Christians exist in real life? If so what was it called? Where can I read about it in detail?
2. What other methods did the government employ to find hidden Christians throughout history?

I think that you are referring to “¥‚ÝŠG

I haven't seen the anime, but the system of "fumi-e" did exist in real life, mainly in the 17th century and vaguely continuing up to the 19th century.
https://en.wikipedia.org/wiki/Fumi-e

Christianity was brought to Japan in the 16th century, and like all other new religions, it was considered as a kind of a cult. It is indeed true that Christianity was often abused in history as a means to start invading land.

But most Christians lived like everybody else, shopping, working and walking around like everybody else. The problem for the government was their faith. So they would use fumi-e. In other words, as long as those people are faithful enough to the local law to be able to step on the Christ figure, there wouldn't be a real problem.

In Japan today, a great percentage of prestigious private high schools are Christian.

2. What other methods did the government employ to find hidden Christians throughout history?

I forgot to answer this question. I don't think there were any other specific "methods", but patrolling around for hidden people while having everybody step on Jesus Christ sounds effective enough to me.

What the Tokugawa shogun government persecuted and weeded out Christians is one thing but why is more important.
Japan was never colonized by Spanish and other European countries s like other South Eastern countries, India to Philippines.
Japanese were trading with other countries freely but the government found out that Europeans send out Christian missionaries to spread the Christianity first, then use them as the spy/informants and brutally conquer the country by deception, slaughtering, desease spreading and empty the treasures as they did in Central and South America and the same was happening in South East Asia. So Japan tried to eliminate the Christians by "Fumi-E" and tightly regulate the trading, called "Sakoku".