Legal analysis: It depends on the case. After general criminal detention, asking family members to sign in the past is to inform family members of detention, and it is possible to sign. But 40 days' detention is unreasonable. If the criminal detention lasts for more than 37 days and the public security organ still does not have the criminal evidence of the criminal suspect, the compulsory measures shall be lifted. It is illegal for the public security organ to continue to detain the criminal suspect, and the criminal suspect or his family members may appeal to the higher authorities of the public security organ.

Legal basis: Criminal Procedure Law of People's Republic of China (PRC).

Article 85 When a public security organ detains a person, it must produce a detention permit. After detention, the detained person shall be immediately sent to the detention center for custody, and shall not exceed twenty-four hours. Unless it is impossible to notify or the notification of suspected crimes endangering national security or terrorist activities may hinder the investigation, the family members of the detained person shall be notified within 24 hours after detention. After the circumstances that hinder the investigation disappear, the family members of the detained person shall be notified immediately.

Article 91 If a public security organ deems it necessary to arrest a detained person, it shall, within three days after detention, submit it to the People's Procuratorate for examination and approval. Under special circumstances, the approval time can be extended by one to four days. For major suspects who commit crimes on the run, commit crimes many times or commit crimes in collusion, the time for submitting for examination and approval may be extended to 30 days. The people's procuratorate shall, within seven days after receiving the approval letter from the public security organ, make a decision on whether to approve or disapprove the arrest. If the people's procuratorate does not approve the arrest, the public security organ shall immediately release it after receiving the notice and promptly notify the people's procuratorate to execute it. Those who need to continue the investigation and meet the conditions of obtaining a guarantor pending trial or residential surveillance shall be granted a guarantor pending trial or residential surveillance according to law.