Field observations published in 2013 and 2015 reported mugger crocodiles in India, and American alligators in Louisiana, resting at the water's edge beneath heron and egret colonies with sticks and twigs balanced on the snout and head. The reports noted the behaviour appeared concentrated in the birds' nest-building season and near colonies, and interpreted it as luring: birds approaching for nest material come within reach.
If that reading is right it would place crocodilians among the few non-avian reptiles credited with using objects as tools, which is why the observations attracted attention.
The criticism is substantial. Sticks and debris routinely accumulate on floating crocodilians, sample sizes were small, controls for drifting vegetation were limited, and no independent replication with rigorous methods has followed. The behaviour is best described as reported and unconfirmed. What is not in doubt is that muggers dig burrows, tolerate reservoirs and canals, and move considerable distances overland when water dries.