Can a Wuxi hukou and a Qijiang hukou get a marriage certificate in Chongqing?

No, you need to go to the civil affairs bureau where your household registration is located

"Marriage Registration Regulations" Article 4 When a mainland resident marries, both men and women shall * * * go through the marriage registration at the marriage registration office where one party's permanent residence is located.

If a China citizen marries a foreigner in the Mainland, and a mainland resident marries a Hong Kong resident, a Macao resident, a Taiwan Province resident or an overseas Chinese in the Mainland, both men and women shall * * * go through the marriage registration office where the permanent residence of the mainland resident is located.

Article 5 When applying for marriage registration, mainland residents shall produce the following documents and supporting materials:

(1) My household registration book and ID card;

(2) A signed statement that I have no spouse and no direct blood relationship with the other party and collateral blood relationship within three generations.

Hong Kong residents, Macao residents and Taiwan Province residents shall submit the following documents and supporting materials when registering for marriage:

(1) My valid passport and ID card;

(2) A statement notarized by the notary office of the place of residence that I have no spouse and no lineal blood relationship with the other party and collateral blood relationship within three generations.