Feb 15 (Reuters) - The Indian rupee came off the day's highs in afternoon trade weighed by dollar demand from local oil refiners, but sharp gains in local shares limited the fall. * Strong dollar inflows also helped the rupee to absorb the impact of selling, traders said. * At 2:39 p.m. (0909 GMT), the rupee was at 49.29/30 to the dollar, stronger than Tuesday's close of 49.36/37, but down from the day's high of 49.19. * Oil refiners are the largest buyers of dollars in the local currency market as India imports more than 80 percent of its oil requirements. * Trading in the local forex market will be shut on Thursday as the state government of Maharashtra, where Mumbai is located, has announced a bank holiday on Thursday for local elections. * India's main share index was up 1.8 percent. (Reporting by Aditya Phatak; Editing by Subhadip Sircar)

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