There is no sin on you if you offer Tarawih at home, because it is a Nafilah (supererogatory prayer). However, it is better to pray it with the Imam in the Masjid following the example of the Prophet (peace be upon him) and his Sahabah (Companions of the Prophet, may Allah be pleased with them). When the Prophet (peace be upon him) led his Sahabah in Tarawih on some nights until the end of the first third of the night, one of them said to him: "We wish that you would lead us in Nafilah Prayer for the rest of the night." He (peace be upon him) replied:
Anyone who prays Qiyam (optional Night Prayer) with the Imam until he finishes it will be recorded for him as spending the whole night in prayer.
Ahmad and the Compilers of the Sunan through a good Isnad [chain of narrators] on the authority of Abu Dhar)
May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family and Companions.