In Letter No. 36 To Jagamohini Dasi, Srila Prabhupada answers two important questions for the servants of Tulasi devi – whether brown or dead leaves can be used in worship, and whether dead branches can be cut.
“…whether we may prune the leaves of Tulasi, no, there is no question of pruning. But you can take for worshiping Krsna leaves from the Tulasi. First utilize the dead leaves or leaves which have fallen down, and if more leaves are required for worshiping Krsna, you may take them from Tulasi plant in this way: First approach Tulasi Devi and offer your obeisances, requesting her that for worshiping Krsna you want to take some leaves. Then if she allows you may take.
There is no question of pruning in the manner of gardeners just to make nice beautiful plant for ornamental purposes. And if there are any dead branches, these may be made into beads, like neck beads, and if they are large branches you can make japa beads. There is no need to keep candle burning all night, but you can burn candle in the evening for one hour for Tulasi Devi, that will be nice.”
Therefore dead leaves can not only be offered, but they should be used BEFORE picking green leaves from Srimati Tulasi devi. “First utilize the dead leaves or leaves which have fallen down, and if more leaves are required for worshiping Krsna, you may take them from Tulasi plant in this way …”
Second, dead branches can be removed and the wood should be used to make neck beads and japa beads. But pruning for appearance should never be done.