Unless you live in a community property state, you can divide your expenses any way on which you both agree. So one person can claim all of the energy credit while the other spouse claims none. 

@IsabellaG And what if you live in a community property state. Can one claim the credit one year and then the other claim the carryover the next year?

No, there needs to be a 50/50 split in the credits and carryovers. No exceptions.

@Rjmartin59  

I'm thinking my spouse and I will file separately. When I do our taxes jointly, we qualify for the $1200 credit but when I do our taxes separately, TurboTax says we each get an $1138.  The credit should be $1200 since the improvements were made to the house we both live in.  How do I adjust the TurboTax amount?

You can't each get the same credit.  

And may I ask why you are filing separate returns?  Sometimes people don't realize the differences between filing  Joint and MFS.

 Here's some things to consider about filing separately……

In the first place you each have to file a separate return, so that's two returns.  And if you are using the Online version that means using 2 accounts and paying the fees twice.  The Desktop CD/Download program would be better to use.

Many people think they come out better when filing Married Filing Separate but they are probably doing it wrong.  If one person itemizes deductions on Schedule A then the other one must itemize too, even if it's less than the standard deduction, even if it is ZERO!  And if you are in a Community Property state it can be complicated to figure out.

And there are several credits you can't take when filing separately, like the

EITC Earned Income Tax Credit

Child Care Credit

Educational Deductions and Credits

And contributions to IRA and ROTH IRA are limited when you file MFS.

Also if you file Married Filing Separately up to 85`% of your Social Security becomes taxable right away even with zero other income.

See …….

https://ttlc.intuit.com/community/married/help/is-it-better-for-a-married-couple-to-file-jointly-or-...

Married filing Separate in Community Property States

https://ttlc.intuit.com/turbotax-support/en-us/help-article/taxation/married-filing-separately-commu...

I'm just doing a comparison to see which filing status would give us the best outcome.

Biden’s new student loan repayment will calculate monthly payments based solely off the actual borrower’s income—  even if married,— but ONLY IF they file taxes as MFS. 
I don’t know if that’s the case with the OP here, but filing this way is about to become very very popular with couples who have student loans 

Depending on the income gap, a spouse could save several hundred—if not thousands-- of dollars a month, drastically outweighing any tax benefits they’d  receive filing jointly.