Yes absolutely if you are renting long term! I am not sure how the monthly rentals provide insurance. You should check into that and see if you are liable for damages?
Last year a friend of mine rented a house while they were remodeling their house. She was cooking with oil and it over heated and burst into flames. The end result it cost him over $40,000 with all the fire, smoke and water damage it caused and that did include the smoke damage to their clothing and furniture. Why take a chance! Renter's insurance is very inexpensive.
Trust me I was in the property claims business for 40 years.
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