Can couples apply for residence permits in a certain district of Chengdu?

Of course. A person has a residence permit and needs to apply for it himself, regardless of whether he or she is a husband or wife. People from other places who come to Chengdu to apply for residence permits are individuals, and both husband and wife need to apply separately. Residence permit is an attempt made by some developed cities in China to learn from the "green card" system of developed countries, which has accumulated experience for China to formulate skilled migration measures and eventually form the national "green card" system of China.