I told the police I might need a lawyer, but they kept asking questions. Can they do that?

On TV, the police make a show of reading the Miranda Rights when they make an arrest.  However, in the real world the police officer may not read you your Miranda Rights until well after the arrest, if at all.  The reading of the Miranda Rights is only required after an arrest if they want to ask questions about the incident for which you were arrested. 

In June 2010 the US Supreme Court made a significant change to the Miranda Right rules.  They ruled that a suspect must clearly tell the police of their intent to remain silent and of their desire for an attorney.  Statements such as "I may need a lawyer" or "I'm not sure I should answer that" do not invoke a suspect's Miranda Rights.  Law Enforcement need  not stop questioning a suspect unless a clear and specific statement invoking Miranda Rights is made. 

If you feel law enforcement questioned you improperly then contact the Law Offices of Richard S Lawson to ensure your rights are protected.