What is the name of your state (only U.S. law)? Louisiana. If I was asked to give a statement and was fingerprinted but was not read my rights can the case be thrown out?
Not based on not being read your rights. If anything, if it was required you were read your rights, the statements obtained could be suppressed. If there is other evidence adequate to prosecute you, then losing your statement means nothing.
depending on the situation, it may not have been required to advise you of your rights prior to the statement. If so, not reading you your rights means nothing.