Best way to create relationship between multiple tables
No, you should not have multiple State tables.  Having a single table with relationships to the others is the right way to approach this.  The perception that this somehow implies that the other tables are linked, other than they share a State, is purely in your head - such an interpretation would not be common practice.

You should distinguish between your logical data model and your physical database design.  I would recommend adding the relationships to State into the logical model.  You may choose to omit the foreign key constraints from your database for performance or other reasons.

There's a post on Dell's Toad site which I can't find just now.  It's about a 200 table DB, every one of which has a UpdateUserId column and corresponding FK relationship to the User table.  The plan for a DELETE User.. statement is a thing of beauty - a perfect left-deep triangle of 200 joins!  They would have been better without the constraint.

Edit: here's the link.  I mis-remembered the details but the principle's the same.