I'm not a sworn LE officer but I have worked in public service jobs & the US military(MPs).
Most agencies & PDs either issue a standard sidearm(holster & ammunition) or authorize a sworn member to buy a firearm/gear from a approved list of brands or vendors.
Many smart PDs, if the have the $$$ or sources, buy a on duty sidearm & a compact 2nd gun/off duty gun with the same carry features. Like a HK P2000 & a HK P2000sk or a Glock 21 & a compact Glock 30 .45acp.
A sworn officer or agent could use full size pistol mags in either model.
BTW: my large county sheriff's office(1200+ sworn members), has used Glock 21s & the Glock 36/23/19 series since 2002 w/o any major problems.
To answer the forum ?; no, most US law enforcement officers do not sign out pistols or sidearms. Shotguns or patrol rifles, yes.
Clyde