The Kusarigama in Ultimate Combat is a double weapon that has two different damage values for each of its weapons. How do I know which weapon does which value?
Kusarigama: "This weapon has a single sickle held in the off-hand attached by 10 feet of fine chain to a weighted metal ball. The sickle is used to make trips, jabs, and blocks while the ball is whipped around at high speeds and then smashed into the opponent."
A medium sickle deals 1d6.
Since a medium Kusarigama is listed as 1d3/1d6, the 1d3 should be the metal ball, and the 1d6 should be the sickle.
However, you're still going to ask your DM how to run the weapon, as it's unclear. I think the RAI is probably that it functions like the Double-Chained Kama, 2-handed reach, or non-reach double weapon. By RAW it's a double weapon with reach, and doesn't really make much sense.
There's a FAQ thread on the Kusarigama here if you're interested.