Probably not. Credit reports and scores are kept separately for each individual. So if you file bankruptcy, the fact that you filed will not show up on your spouse's credit report on the "public record" section of the report.
On the part of your credit report that lists your debts, the "tradeline" section, the story is a little different.
If you have "joint" credit accounts, that you are both liable to pay, then the creditor can still seek to collect the debt from the non-filing spouse. They can also continue to report the status of the debt on the non-filing spouse's credit. So to preserve their credit, the non-filing spouse would have to timely pay the debt.
Also, if your non-filing spouse (or someone else) is an "authorized user" on one of the credit cards that you intend to list in your bankruptcy, you want to have them removed, if possible, before you file bankruptcy. Otherwise, the account will show it was discharged in bankruptcy on their credit report.
As a practical matter, it is often better for both spouses to file bankruptcy together, to get a fresh start for the both of them. Your credit scores can recover quickly after a bankruptcy, and it is usually little or no more expensive on the attorney fees for both spouses to file together.