Cops are allowed to go through your mail if your mail has been thrown out to the curb and is in the trash or if the cop has a warrant to go through your mail.
However if the mail is not in the trash and the cops don't have a warrant, the cops cannot just go through your mail or go through your mailbox to look through your mail.
The police could get a search warrant and search the mail in your mailbox or at the post office or search the mail inside your house.
But without the search warrant to go through your mail, the cops and police cannot simply go through your mail.
That is unless, your mail is placed in the trash or recycling bin.
Just like anybody else can go through your trash or recycle bins that is outside your house on the curb, the police can also do so.
Trash, especially that is at the curb is considered by law to be in the public domain and once you place something in your trash or at the curb for trash pickup, you gave up the rights to those items.