Can carrying charges (investment management fees) for a joint account be shared or can only one person claim it?

It depends on how the income itself will be claimed and how the investments were started.

If you put in all of the money for the investment, you'll claim all of the gains/losses and all of the expenses. If you and another person split the original investment 50/50, you'll each claim 50% of the gains/losses and 50% of related expenses.

Does each spouse enter 100% of the carrying costs, and Turbotax will spit it, or do I split it and enter 50% for each spouse?