Does it matter if the police station handles the hotel check-in certificate?

It doesn't matter if the police station handles the hotel check-in certificate. Generally, no one will know that you have handled it. This is personal privacy, and it can't be found without legal procedures.

The police station will fill in a personal identity information form when checking in at the hotel, and write down the name, household registration address, ID number and other related information. After the police check that the information is correct, they will issue identification certificates, which can be used to stay in hotels and restaurants.

According to Article 6 of the Measures for the Administration of Public Security in Hotel Industry, hotels must register for receiving passengers' accommodation. At the time of registration, the passenger's identity documents shall be checked and truthfully registered according to the prescribed items. Accommodation registration form shall be submitted to the local public security organ within 24 hours for receiving overseas tourists.