Developing thick woody trunks and stems, a croton (Codiaeum variegatum) becomes an upright, rounded shrub with waxy, leathery leaves. Grown as a houseplant in cold climates, it loses its foliage and branches die back when exposed to subfreezing temperatures.
The best time to cut back a croton is in the warmth of mid spring to early summer. This allows ample time in summer for buds to sprout and reveal new leaves before the temperatures cool and the plant drastically slows its growth rate. Prune dead or broken branches of croton any time of year. Make the pruning cut 1/2 inch above a lower branch junction or leaf. Cutting back into bare wood is also OK, as dormant leaf/stem buds below the cut eventually sprout.
The Croton Society website says to cut back 1/3 of all branches on the croton shrub if you wish to create a bushier, more rounded plant. Next year cut back an additional 1/3 of the oldest, leggiest branches. Although it's likely new branches and leaves would sprout if you hacked the plant back to its trunk, the regrowth would be tightly clustered and require more thinning to train into an even, well-branched shrub.
Wear rubber or other thick gloves when pruning croton since a milky sap quickly exudes from branches and leaves. In some people a skin rash develops with contact. Remove branches by moving them horizontally out of the shrub rather than lifting branches up out of the plant. This diminishes sap drip onto remaining leaves as well as onto your clothes or other exposed skin.