I invested in my mother's house which was in a reverse mortgage. She died without a will. Can I sell the house?

Did your mother add your name to the title (deed)? If so, you have to read the deed carefully. If your mother conveyed the property to herself and you as "joint tenants," then you are now the sole owner of the property. If the deed reads "tenants in common," then since your mother did not leave a will, her share of the house goes to her heirs (if your father is also deceased, her heirs would be you and any siblings you may have). The same is true if your mother never put your name on the deed. In either case, you will probably have to file a proceeding in the probate court in order to get title to the house legally transferred to you and any other of your mother's heirs. I highly recommend that you see a probate attorney immediately because all of the above is complicated by the reverse mortgage.