We have a shared septic system for 6 home condo that failed. We shared the cost of replacement. Can each house owner claim the credit of $6000 for their share of cost ?

Sorry----repairs to the septic system for your own residence are not deductible.  Or are you the owner of all the condos----are you the landlord who rents out the other five condos to tenants?

This is a Massachusetts state tax credit.  Here is what I found using Google - https://www.mass.gov/technical-information-release/tir-97-12-personal-income-tax-credit-for-failed-cesspool-or-septic-system-title-5-expenditures

Hi, I am just one of the owner of 6 single family homes in the condo association.  The other 5 homes are owned by different individual owners.  

Then---sorry---you simply have a personal expense that is not deductible on a federal tax return.  Your state laws might be different.

This is not true.  I spoke to MA state department pf revenue and they confirmed it is deductible upto $6000 of septic failure project.