Does putting my house in a trust save on taxes?

If you're using a revocable living trust, (where you can change the trust and you keep possession of the house), then the local property tax assessor will ignore the trust and send you the annual property tax bill, while you're alive. So there's no property tax savings by putting your house into this trust.

When this revocable living trust sells the house before your death, the IRS will ignore the trust and you can use the $250k ($500k if married) home sale exemption just like you would if the house was not in a trust. (see https://www.carrolltaxfirm.com/post/income-tax-on-the-sale-of-your-home). So there's no income tax savings if you sell the home before you die with your house in this trust.

When the now-irrevocable trust sells the house after your death (now irrevocable because you're dead and can't change it), then the IRS will tax the trust on the gain (the difference between the sale price and the date-of-death house value). The IRS could instead tax the trust beneficiaries (perhaps your kids) if the trust is written to allow this. (see https://www.carrolltaxfirm.com/post/should-an-estate-asset-be-sold-after-it-is-distributed-to-estate-beneficiaries-or-before). So there's a potential larger income tax bill if the trust sells the home after you die and you have not written the trust properly.

If the revocable trust distributes the house to its beneficiaries and they then sell the house, the IRS will tax the trust beneficiaries on the gain using, again, the difference between the sale price and the date-of-death house value. So there's no income tax savings if the house is sold after your death by your trust beneficiaries.

Most people put their house into a trust to allow the house ownership to transfer to their children without probate court approval. But when the children want to sell the house, they will need probate court approval. Connecticut houses, formerly owned by an individual or revocable trust, must have proof that the estate of the deceased person that created the trust owes no estate taxes. Only a probate court can provide that proof. So title can transfer from you (your trust) to your children but cannot transfer from your children to third-parties without probate court approval.

The alternative to the revocable trust is an irrevocable trust where you would relinquish power over the trust and therefore over your house. The probate court would not be involved BUT if this trust sells your home after you die, the trust (which already pays a higher tax than an individual) will be taxed based on the difference between the sale price and the house value when the trust was created. So there's no step-up in basis at death with this irrevocable trust but you avoid probate approval. I see this trust used when someone is preparing to enroll in medicaid and title 19.