Does Turbo Tax Calculate CUTMA returns?

You mean The Uniform Gifts to Minors Act (UGMA) and the Uniform Transfers to Minors Act (UTMA)?

See this answer concerning UTMA - <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/4329796-as-an-utma-custodian-do-i-file-separate-returns-for-the-minor-or-include-the-information-on-my-return">https://ttlc.intuit.com/questions/4329796-as-an-utma-custodian-do-i-file-separate-returns-for-the-minor-or-include-the-information-on-my-return</a>

First you decide whether your report the child's investment income on your FEDERAL tax return or file a separate tax return for the child.

If his only income is from interest and dividends,  or capital gains distributions shown on a 1099-DIV, there is a provision for entering it on your return, using form 8814. Enter at Less common income / Child's income. Otherwise, the child must file his own return, if he has sufficient income.

If you file the child's income on your return, Calif. also has a provision for filing it  on your state return.  See <a rel="nofollow" target="_blank" href="https://www.ftb.ca.gov/individuals/FileRtn/7.shtml">https://www.ftb.ca.gov/individuals/FileRtn/7.shtml</a>,

If not, you will have to file separate  state and federal returns, so your question may be academic.

I don't  know if TurboTax can handle  that (CA form  FTB 3800), but  I have flagged your question for the TT moderators.

Yes, TurboTax supports it. It's in the forms availability list for California. The form number on the form, and in the TurboTax list, is just 3800, not FTB3800. But the California instructions refer to it as FTB 3800.

 See https://www.ftb.ca.gov/individuals/FileRtn/7.shtml, which says, in part:

For taxable years beginning on or after January 1, 2010, California law conforms to federal law which allows parents’ election to report a child’s interest and dividend income from children under age 19 or a student under age 24 on their tax return. For each child under age 19 or student under age 24 who received more than $2,100 of investment income in 2018, complete Form 540 and Form FTB 3800, Tax Computation for Certain Children with Investment Income, to figure the tax on a separate Form 540 for your child.