They do. But state laws and police department policies can go further than the federal constitution requires. Your statement as to how you did your job I’m guessing reflected your department’s policy. It was certainly not a statement of what the Constitution demands. Under the Constitution, an arrest does not require a warrant or a signed complaint by someone for all arrests.
The Constitution does probable cause to believe the defendant committed a crime before making teh arrest and an arrest warrant is generally required to enter upon private premises to make the arrest. But some states and police departments will have additional requirements for their officers to meet before making an arrest, and yours was evidently one of those.

