Well, I wasn't sure on this one, so I had to look it up. I found some New Jersey laws about Dum Dum Ammunition, and wasn't sure how to proceed on this one. (I felt dum dum, and had to laugh!)

"Expanding bullets were given the name Dum-dum, or dumdum, after an early British example produced in the Dum Dum Arsenal, near Calcutta, India by Captain Neville Bertie-Clay.[6][7][8] There were several expanding bullets produced by this arsenal for the .303 British cartridge, including soft-point and hollow-point designs. These were not the first expanding bullets, however; hollow-point expanding bullets were commonly used for hunting thin-skinned game in express rifles as early as the mid-1870s.[9] The use of the term "Dum-dum" applied to expanding bullets other than the early .303 designs is considered slang by most ammunition and ballistics sources.[10][11] Manufacturers have many terms to describe the particular construction of the various types of expanding bullets, though most fall into the category of soft-point or hollow-point designs. The expansion itself is sometimes called mushrooming."

Strictly speaking, I believe the term specifically applies to military ammunition, as expanding bullets are generally banned by the Geneva Convention.

Technically, the Geneva Convention does not address this issue.
They are banned by the 1899 Hague Declaration, however.

I think Chad's note is pretty spot on. Dum-Dum is basically a slang term for an expanding bullet, not necessarily restricted to military usage.

Police in the US use them since, being strictly domestic, they're not governed by international law.

So a dum dum bullet is a hollow point. Are you saying that New Jersey won't let you have hollow point bullets?!?

I always thought dumdums were frags, I never bothered to look it up once the internet came around. I don't think I've heard that term in over 40 years.

I had read a report of a “Dum Dum” bullets impact results on one of Teddy Roosevelt’s officers during the Spanish American war.

The bullet was described as being a “Mauser FMJ bullet that had been modified to expand by cutting the tip off to expose the core and initiate violent expansion.”