From my experience having been arrested and held like this before: No. They don't even have to attest to probable cause until the 24-hr limit hits, in which case they will then formally arrest you by taking you to be fingerprinted, a reading of Miranda, etc along with paperwork containing the attestation of probable cause, or let you go, again, with a pile of paperwork, and sometimes both, in which case they arrest you formally, give you paperwork, and an issued summons to appear in court before sending you on your way.