If in the agreement there is a clause for appointment of an arbitrator for any disputes, then you cannot approach civil court if an arbitrator has been appointed.
However there is a Kerala high court verdict on this which has a different thing to tell, which is given below:
Going by Section 8 of the Arbitration and Conciliation Act, I am of the opinion that mere inclusion of an arbitration clause in the agreement does not bar or cause to oust the jurisdiction of the civil court provided Under Section 9 of the Code of Civil Procedure. The above view is further supported by Section 5 of the Arbitration and Conciliation Act, which says that "in the matters governed by first part of the Arbitration and Conciliation Act, no judicial authority shall intervene except where so provided in the first part". It means that jurisdiction of the Civil Court is not completely ousted by Section 8 of the Arbitration and Conciliation Act. Section 5 of the Arbitration and Conciliation Act does not bar the exercise of general power of the civil court to grant interim relief including specific injunctive relief Under Order XXXIX of the Code of Civil Procedure and the Specific Relief Act....”
The Supreme Court disagreed with the views of High Court and held as following
“Once an application in due compliance of Section 8 of the Arbitration Act is filed, the approach of the civil court should be not to see whether the court has jurisdiction. It should be to see whether its jurisdiction has been ousted. There is a lot of difference between the two approaches. Once it is brought to the notice of the court that its jurisdiction has been taken away in terms of the procedure prescribed under a special statue, the civil court should first see whether there is ouster of jurisdiction in terms or compliance of the procedure under the special statute. The general law should yield to the special law-generalia specialibus non derogant. In such a situation, the approach shall not be to see whether there is still jurisdiction in the civil court under the general law. Such approaches would only delay the resolution of disputes and complicate the redressal of grievance and of course unnecessarily increase the pendency in the court”
The latest judgement of the Supreme Court would apply to only those suits/proceedings wherein both the parties are bound by Arbitration agreement, however where the one of reliefs/parties is outside the scope of arbitration clause, Civil Court shall have the jurisdiction to entertain the suit, notwithstanding the Arbitration clause with some of the parties, in view of earlier judgement of Supreme Court in the matter of Sukanya Holding Private Limited Vs. Jayesh H Pandya, AIR 2003 SC 2252, wherein it was held as follows
"If a suit is filed against parties, some of which are bound by the Arbitration agreement, while others are not, in such circumstances a common suit will lie against the parties. Two different remedies in respect of same cause of action are not maintainable"